{"id":12405,"date":"2019-12-17T16:19:46","date_gmt":"2019-12-17T10:49:46","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=12405"},"modified":"2021-07-02T15:36:29","modified_gmt":"2021-07-02T10:06:29","slug":"1st-puc-statistics-question-bank-chapter-6","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-statistics-question-bank-chapter-6\/","title":{"rendered":"1st PUC Statistics Question Bank Chapter 6 Analysis of Bivariate Correlation and Regression"},"content":{"rendered":"

You can Download Chapter 6 Analysis of Bivariate Correlation and Regression Questions and Answers, Notes, 1st PUC Statistics Question Bank with Answers<\/a> Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 1st PUC Statistics Question Bank Chapter 6 Analysis of Bivariate Correlation and Regression<\/h2>\n

1st PUC Analysis of Bivariate Correlation and Regression Two Marks Questions and Answers<\/h3>\n

Question 1.
\nWhat is correlation?
\nAnswer:
\nCorrelation is said to exists between two variables if they vary directly or indirectly together.<\/p>\n

Question 2.
\nMention different types of correlation.
\nAnswer:<\/p>\n

    \n
  1. Positive correlation<\/li>\n
  2. Negative correlation<\/li>\n
  3. zero correlation<\/li>\n<\/ol>\n

    Question 3.
    \nGive examples for different types of correlation.
    \nAnswer:<\/p>\n

      \n
    • Demand and supply, Height and weight -positive correlation<\/li>\n
    • Price and demand, price and sales-negative correlation<\/li>\n
    • Height or Weight of a student and marks obtained in an exam-zero correlation<\/li>\n<\/ul>\n

      Question 4.
      \nDefine the co-efficient of correlation
      \nAnswer:
      \nThe degree or the extent of the correlation that exists between the variables is called coefficient of correlation, denoted by gamma (\u03b3).<\/p>\n

      \"KSEEB<\/p>\n

      Question 5.
      \nWhat is scatter diagram?
      \nAnswer:
      \nWhen the values of the two variables are plotted on graph on an xy-plane, the spread or the scattered ness of the plotted points gives the types of correlation and the degree of the correlation that exists between the variables, the diagrams is called scattered diagrams.<\/p>\n

      Question 6.
      \nDefine positive correlation and negative correlations.
      \nAnswer:
      \nThe two variables are said to be positively correlated if they vary in the same direction, eg., demand and supply and, the two variables are said to be negatively correlated if they vary in the opposite direction, eg., price and sales.<\/p>\n

      Question 7.
      \nWhat is causation?
      \nAnswer:
      \nThe cause and effect relationship between the two correlated variables is called causation.<\/p>\n

      Question 8.
      \nWhat is spurious correlation?
      \nAnswer:
      \nThe absence of causation between two variables even though they vary together is called spurious correlation.<\/p>\n

      Question 9.
      \nWrite down any two properties of coefficient of correlation.
      \nAnswer:<\/p>\n

        \n
      • It is independent of units of measurement<\/li>\n
      • It is independent of origin and the scale.<\/li>\n<\/ul>\n

        Question 10.
        \nWhat is the range of correlation co-efficient?
        \nAnswer:
        \n\u03b3 = \u00b11 ie., it can take the least value -1 and the highest value +1<\/p>\n

        Question 11.
        \nWhat is the value of co-efficient correlation for any two independent variables?
        \nAnswer:
        \n\u03b3 = 0<\/p>\n

        Question 12.
        \nDefine Rank correlation.
        \nAnswer:
        \nThe ordinary co-efficient of correlation between the two ranking variables OR the product moment co-efficient correlation between the two ranking variables is called rank correlation, denoted by ‘p’\/R<\/p>\n

        Question 13.
        \nWrite any difference between correlation and Rank correlation.
        \nAnswer:
        \nCorrelation is the measure of relationship between two quantitative characteristics called variables, such as ht. & wt, age & wt, of persons, ages of husbands and wives etc.,Where as the Rank correlation is the measure of relationship of two qualitative characteristics called attributes, such as the aesthetic senses as IQ, Beauty, Intelligence, Taste etc between the persons.<\/p>\n

        Question 14.
        \nDefine the term regression.
        \nAnswer:
        \nRegress means go back to the origin, regression means estimation of unknown value of a given variable by knowing all values of the other variable when the variables are correlated<\/p>\n

        Question 15.
        \nWhat are regression equations? And write down the two regression equations.
        \nAnswer:
        \nThe functionai relation developed between the two correlated variables are called regression equations.
        \nThe regression equation of x on y is: (X – X\u0304) = bxy<\/sub> (Y – \u0232) where bxy-the regression coefficient of x on y.
        \nThe regression equation of y on x is: (Y – \u0232) = bxy<\/sub> (X – X\u0304) where byx-the regression coefficient of y on x.<\/p>\n

        \"KSEEB<\/p>\n

        Question 16.
        \nWhat are regression lines?
        \nAnswer:
        \nThe graph of regression equations are called regression lines.<\/p>\n

        17.
        \nWhat are regressions co-efficient?
        \nSol.
        \nbxy<\/sub> and byx<\/sub> are called regression co-efficients.<\/p>\n

        18.
        \nWrite the properties of regression lines.
        \nSol.<\/p>\n

          \n
        • The two regression lines coincides at \\((\\bar{x}, \\bar{y})\\)<\/li>\n
        • The two regression lines intersect when there is a perfect correlation.<\/li>\n
        • The two regression lines are perpendicular to each other when there is no correlation.<\/li>\n<\/ul>\n

          19.
          \nWrite the properties of regressions co-efficients.
          \nSol.<\/p>\n

            \n
          • The regression co-efficients are independent of the origin but dependent on the scale.<\/li>\n
          • The geometric mean of the two regression co-efficients is numerically equal to the co-efficient of correlation, ie., \\(r=\\pm \\sqrt{b_{x y} \\times b_{y x}}\\)<\/li>\n
          • Since the r cannot be greater than 1, so the product of the two regression co-efficients never exceeds 1.<\/li>\n
          • If the value of one of regression co-efficient is greater than 1 and the other should be less than 1.<\/li>\n<\/ul>\n

            1st PUC Analysis of Bivariate Correlation and Regression Problems<\/h3>\n

            Question 1.
            \nDraw a slatter diagram or the following data ant common on correlation.
            \n\"1st
            \nAnswer:
            \n\"1st
            \nFrom the diagram, the scatterd points shows raising straight line. There exists a high degree positive correlation between price and supply.<\/p>\n

            Question 2.
            \nDraw a scatter diagram for the following data and interpret it.
            \n\"1st
            \nAnswer:
            \n\"1st
            \nFrom the scattered diagram, the spraded for the points show down ward diagram. Hence x and y are negatively correlated.<\/p>\n

            Question 3.
            \nThe following data gives the age of a motor cycle and the annual maintenance cost over a period. Find the product moment coefficient of correlation and interpret the same.
            \n\"1st
            \nAnswer:
            \nLet x and y be the age and maintenance cost, the data is small in size, so use direct method.<\/p>\n

            \"1st
            \n\"1st
            \n\u2234 There exists a high degree positive correlation.<\/p>\n

            Question 4.
            \nCalculate karl pearson’s coefficient of correlation between x and y.<\/p>\n

            \"1st
            \nAnswer:
            \nThe data is large in size, so use step deviation or short cut method.<\/p>\n

            \"1st
            \nwhere A, B assumed means and C – common factors from x and y.
            \n\"1st
            \nHere \u03b3 > 0.5. The exists high degree or close to perfect positive correlation.<\/p>\n

            \"KSEEB<\/p>\n

            Question 5.
            \nFind K.P.C.C of the following data
            \n\"1st
            \nAnswer:
            \nLet X and Y be ages of husbands and wifes. Here by observation method, Arithmetic means are Whole numbers\/ integers. 50, it is convenient to use actual mean method
            \n\"1st<\/p>\n

            Question 6.
            \nCalculate the coefficient fo correlation between the number of children and age of mothers from the following bivariate frequency table.
            \n\"1st
            \nAnswer:
            \nLet x and y be the ages of mothers and number of children.
            \nThe data is discrete nature for y and with a common difference in x:<\/p>\n

            \"1st
            \n\"1st
            \n\"1st
            \nThere exists a high degree negative correlation between ages of mothers and number of children.<\/p>\n

            Question 7.
            \nCalculate the karl pearson’s coefficient of correlation between ages of students and marks obtained in a certain test and interpret.
            \n\"1st
            \nAnswer:
            \nLet x and y be the marks and age
            \n\"1st\"1st\"1st
            \nHere, there exists high degree negative correlation between Age of students and their marks.<\/p>\n

            Question 8.
            \nCalculate K.P.C.C from the following date.
            \n\"1st
            \nAnswer:
            \nBoth variables are continuous so, use step deviation method.<\/p>\n

            \"1st<\/p>\n

            Question 9.
            \nIf the covariance between x and y variables is 12.5 and variance of x and y are respectively 16.4 and 13.8. Find the coefficient of correlation between them.
            \nAnswer:
            \n\"1st
            \n\"1st<\/p>\n

            Question 10.
            \nGiven COV (x,.y) = -30, Var (x) = 225 and Var (y) = 9, find karl pearson’s coefficient of correlation.
            \nAnswer:
            \n\"1st<\/p>\n

            \"KSEEB<\/p>\n

            Question 11.
            \nIn a bivariate data, if standard deviations of x and y are 5 and 9 respectively. If the COV (x, y) = 8, find the coefficient of correlation.
            \nAnswer:
            \n\"1st<\/p>\n

            Question 12.
            \nIn a bivariate \u03a3(x – x\u0304)2<\/sup> = 35, \u03a3(x – x\u0304)2<\/sup> = 60, \u03a3(x – x\u0304)(y – \u0233) = 42. Find the coefficient of\u00a0 correlation
            \nAnswer:
            \n\"1st<\/p>\n

            Question 13.
            \nIn a bivariate data \u03a3xy = 500, \u03a3x = 15, \u03a3y = 200, \u03a3x2<\/sup> = 98, \u03a3y2<\/sup> = 23250 and n = 10. Find the coefficient of correlation.
            \nAnswer:
            \n\"1st<\/p>\n

            Question 14.
            \nThe coefficient of correlation between two variables x and y is 0.65, their covariance is 2.32. The variance of x is 18. Find standard deviation of y.
            \nAnswer:
            \n\"1st<\/p>\n

            Question 15.
            \nIf the coefficient of correlation between x and y is ‘o’ comment.
            \nAnswer:
            \nIf \u03b3 = 0. the two variables x and y are independent, i.e., Non correlated.<\/p>\n

            Question 16.
            \nDefine spurious correlation.
            \nAnswer:
            \nAbsence of causation between the variables is called sparious correlation.<\/p>\n

            Question 17.
            \nCalculate spearman’s rank correlation for the following data regarding sports and studies of 8 students:
            \n\"1st
            \nAnswer:
            \nRanks are given. Let R1<\/sub> and R2<\/sub> be the ranks in sports and studies.
            \n\"1st
            \nThere exists low degree negative correlation between sports and studies.<\/p>\n

            Question 18.
            \nTen competitors in a pointing competition are ranked by two judges. Using rank correlation find out whether the two judges have common table in painting:<\/p>\n

            \"1st
            \nAnswer:
            \nRanks are given. Let R1<\/sub> and R2<\/sub> be the ranks of judges I and II
            \n\"1st
            \nthe two Judges have high degree of similar taste in beauty of paintings.<\/p>\n

            \"KSEEB<\/p>\n

            Question 19.
            \nThe corresponding values of 2 series are given below.<\/p>\n

            \"1st
            \nFind the coefficient of rank correlation of the above series.
            \nAnswer:
            \nRanks are not given. We have to assign rank. Assign ranks R1<\/sub> and R2<\/sub> for the variables x and y in descending order as highest value as 1, 2, upto 7.
            \n\"1st
            \nThere exsits a high degree positive correlation<\/p>\n

            Question 20.
            \nCalculate rank correlation from the following marks in Accountancy and statistics
            \n\"1st
            \nAnswer:
            \nRanks are not given. Assign ranks as R1<\/sub> and R2<\/sub> for the marks in Accountancy and statistics as 1st<\/sup> who got highest marks and 2nd<\/sup> to next less marks.
            \n\"1st
            \nThere exists low degree correlation between marks in Accountancy and Statistics.<\/p>\n

            Question 21.
            \nCalculate rank correlation coefficient from the following data:<\/p>\n

            \"1st
            \nAnswer:
            \nHere the values of the variables are repeated,
            \nSo use, the formula:
            \n\"1st
            \nm1<\/sub> = 3 (65 repeated 3 times)
            \nRanks are averaged as = \\(\\frac{6+7+8}{3}=7\\)<\/p>\n

            m2<\/sub> = 2(13 repeated 2 times)
            \nRanks are averages as = \\(\\frac{4+5}{2}=4.5\\)
            \n\"1st
            \n\"1st
            \nThere exists high degree positive correlation between x and y.<\/p>\n

            Question 22.
            \nCalculate coefficient of correlation undere rank difference method for the following data<\/p>\n

            \"1st
            \nAnswer:
            \nRepeated values in the variables, so use correation factor formula.
            \n\"1st
            \nm – available repeated number of times
            \nLet R1<\/sub> and R2<\/sub> be the ranks of variables x and y.
            \n\"1st
            \nThere exsits a low degree positive correlation between the variables.<\/p>\n

            Question 23.
            \nMention the uses of Rank correlation.
            \nAns.
            \nSpearman’s rank correlation useful<\/p>\n

              \n
            • To find the correlation between two qualitative characteristics, such as Honesty, Intelligence, Taste etc.<\/li>\n
            • This method is easy and simple as compared to karl pearsons method when the data has no repetitions.<\/li>\n<\/ul>\n

              Question 24.
              \nWhen do you use Rank method of correlation?
              \nAns.
              \nRank method of correlation is used to find correlation between two qualitative characteristics.<\/p>\n

              Question 25.
              \nThe coefficiently rank correlation is 0.75 and the sum of the squares of the difference in rank is 30, then find the value of V.
              \nAnswer:
              \nGiven: p = 0.75, \u03a3d2<\/sup> = 30
              \n\u2234 \\(r=1-\\frac{6 \\Sigma d^{2}}{n^{3}-n}\\) \\(0.76=1-\\frac{6 \\times 30}{n^{3}-n}\\)
              \n\\(\\frac{180}{n^{3}-n}=1-0.75=0.25\\)
              \n\\(\\frac { 180 }{ 0.25 }\\) = n3<\/sup> – n 720 = n3<\/sup> – n
              \n9 \u00d7 80 = n(n2<\/sub> – 1) 9(81 – 1) = n(n2<\/sup> – 1)
              \n9(92<\/sup> – 1) = n(n2<\/sup> – 1) \u2234 n= 9<\/p>\n

              Question 26.
              \nIf n = 10 and \u03a3d2<\/sup> = 200, find the coefficient of rank correlation.
              \nAnswer:
              \n\"1st<\/p>\n

              Question 27.
              \nIf \u03a3d2<\/sup> = 182 and r = -0.1030 find ‘n’
              \nAnswer:
              \n\\(\\mathrm{r}=1-\\frac{6 \\Sigma d^{2}}{n^{3}-n} \\quad-0.1030=1-\\frac{6 \\times 182}{n^{3}-n}\\)
              \n\\(\\frac{1092}{n^{3}-n}=1+0.1030=1.103 ; \\quad n^{3}-n=\\frac{1092}{1.103}\\)
              \nn3<\/sup> – n = 990 = 10 \u00d7 99; n(n2<\/sup> – 1) = 10(100 – 1)
              \nn(n2<\/sup> – 1) = 10(102<\/sup> – 1); \u2234 n = 10<\/p>\n

              \"KSEEB<\/p>\n

              Regression\u00a0<\/strong><\/p>\n

              Question 28.
              \nFrom the following data:
              \n(a) Calcualte the regression equation of x on y.
              \n(b) Estimate the value of x when y = 40.
              \n\"1st
              \nAnswer:
              \nRegression equation x on y is :
              \n(x – x\u0304) = bxy <\/sub>(y – \u0233)
              \nHere, x and y variables have their Arithmetic means with whole number \/ integers. So, it is convenient to use actual mean method.
              \n\"1st\"1st
              \n\\(n=5 ; \\bar{x}=\\frac{140}{5}, \\bar{y}=\\frac{80}{5}=16\\)
              \nbxy<\/sub> = \\(\\frac { 160 }{ 160 }\\) = 1<\/p>\n

              (a) Regression equation of x on y is
              \nx – 28 = 10-16)
              \nx = y- 16 + 28 \u2234 x = y + 12<\/p>\n

              (b) Estimation of x when y = 40
              \nx = 40 + 12 = 52<\/p>\n

              Question 29.
              \nFrom the following data of the age of Husband (x) and the age of the wife (x) obtain the regression equation of y on x and calculate the wife’s age (y). When husband’s age(x0’s 25 years.
              \n\"1st
              \nAnswer:
              \nRegression equation y on x is (y – \u0233) = byx <\/sub>(x – x\u0304)
              \nHere x and y variables Arithmetic means are not in whole numbers\/ integers. So, it is better to use shortcut method.
              \n\"1st\"1st\"1st
              \nRegression equation of y on x is:
              \ny – 24.8 = 1.35 (x – 32)
              \ny -24.8 = 1.35x – 1.35 \u00d7 32
              \ny = 1.35x- 43.2 + 24.8
              \n\u2234 y = 1.35x – 18.4
              \nEstimation of (y) wife’s age when husbands age (x) is 25:
              \ny = 1.35 (25) – 18.4 = 33.75 – 18.4
              \ny = 15.35 years.<\/p>\n

              Question 30.
              \nConstruct two regression equations for the following data and estimate the value of x when y = 70 and y when x = 650.
              \n\"1st
              \nAnswer:
              \nThe two regression equations are:
              \nRegression equation of x on y : (x – x\u0304) = bxy <\/sub>(y – \u0233)
              \nRegression equation of y on x : (y – \u0233) = bxy <\/sub>(x – x\u0304)
              \nBoth variables having common differences, so use step deviation methods.
              \n\"1st<\/p>\n

              \"1st
              \nHere ix<\/sub> common width in x = 100
              \niy<\/sub> common width in v = 10 and n = 7;
              \n\"1st
              \nRegression equation of x on y:
              \nx – 400 = 6.05 (y-80) = 6.05y-605 \u00d7 80
              \nx = 6.05y – 48.4+ 400<\/p>\n

              Regression equation of x on y : (x – x\u0304) = bxy <\/sub>(y – \u0233)
              \nx – 14 = 1(y – 8)
              \nx = y – 8 + 14
              \n\u2234 x = y + 6<\/p>\n

              and regression equation y on x is : (y – \u0233) = bxy <\/sub>(x – x\u0304)
              \ny – 8 = 0.8695 (x – 14)
              \ny = 0.8695x – 12.173 + 8
              \n\u2234 y = 0.8695x -4.173
              \nEstimation of x when y = 20.
              \n\u2234 From the Regression equation of x on y:
              \nx = 20 + 6 = 26
              \nWe know that the coeffiicent of correlation:
              \n\\(\\gamma=\\pm \\sqrt{b_{x y} \\cdot b_{y x}}=\\sqrt{1 \\times 0.8695}=0.9325\\)<\/p>\n

              \"KSEEB<\/p>\n

              Question 31.
              \nEight observations on each of two variables x and y are given below:
              \n\"1st
              \n1. obtain two regression equation and
              \n2. Find \u03b3xy<\/sub>
              \nAnswer:
              \n\"1st\"1st
              \n\u2234 x = 6.05y – 84
              \npregression equation of y on x:
              \ny – 80 = 0.1643(x – 400)
              \n= 0.1643x – 0.1643 \u00d7 400
              \n= 0.1643x – 65.72+80
              \n\u2234 y = 0.1643x + 14.28
              \nEquation y when x = 70
              \nx = 605 (70) – 84 = 423.5 – 84
              \n\u2234 x = 339.5
              \nEquation y when x = 650
              \ny = 0.1643(650) + 14.28 = 106.795 + 14.28
              \ny = 121.075<\/p>\n

              Question 32.
              \nCalculating the regression equation of x on y and y on x from the following data and estimate x when y = 20. Also determine the value of correlation coefficient.
              \n\"1st
              \nAnswer:
              \nThe values of x and y varibles are small in size so, use direct method for easy calculation.<\/p>\n

              \"1st\"1st
              \nRegression coefficient of x on y: (x – x\u0304) = bxy <\/sub>(y – \u0233)
              \nx – 2.5 =0.4762 (y – 4.5)
              \n= 0.4762y – 0.4762x
              \nx = 0.4762y – 2.1429 + 2.5
              \n\u2234 x = 0.4762j + 0.3571<\/p>\n

              Regression equation of y on x = (y – \u0233) = bxy <\/sub>(x – x\u0304)
              \ny – 4.5 = 2(x – 2.5)
              \ny = 2x – 2 \u00d7 2.5 + 4.5
              \ny = 2x – 5 + 4.5
              \n\u2234 = 2x – 0.5<\/p>\n

              We know the relation between coefficient of correlation and the regression coefficients:
              \n\\(\\gamma=\\pm \\sqrt{b_{x y} \\cdot b_{y x}}=\\sqrt{0.4762 \\times 2}\\)
              \n\u03b3 =0.9759<\/p>\n

              Question 33.
              \nCalculate the two regression equations from the following bivariate table and determine y.<\/p>\n

              \"1st
              \nAnswer:
              \nFor Bivariate, both x andy variables having common differences. So use step deviation method:
              \n\"1st\"1st
              \nRegression equation of x on y : (x – x\u0304) = bxy <\/sub>(y – \u0233)
              \nx – 25 = 0.256 (y – 19.8)
              \n= 0.256y – 0.256 \u00d7 19.8x
              \n=0.256y – 5.0688 + 25
              \n\u2234 x = 0.256y + 19.9312<\/p>\n

              Regression equation of y on x = (y – \u0233) = bxy <\/sub>(x – x\u0304)
              \ny – 19.8 = 0.667(x – 25)
              \n\u2234 = 0.6667x – 0.667 \u00d7 25
              \ny = 0.6667x – 16.675 + 19.8
              \n\u2234 y = 0.667x + 3.125
              \nand \\(\\gamma=\\pm \\sqrt{b_{x y} \\cdot b_{y x}}=\\sqrt{0.256 \\times 0.667}\\)
              \n\u03b3xy <\/sub>= 0.4132<\/p>\n

              \"KSEEB<\/p>\n

              Question 34.
              \nObtain the regression equation of y on x and hence estimate y when x = 32
              \nAnswer:
              \n\"1st
              \n\"1st
              \nChoose A and B the assumed means as : A = 25, and B = 27.5 from the respective mid points of the variables x and y width x: ix = 10 and width y : iy = 5
              \n\"1st
              \n\"1st
              \nRegression equation of y on x
              \n4 – 34.5 = 0.723 (x – 38.667)
              \n= 0.723 x – 27.96 + 34.5
              \ny = 0.723 x – 27.956+ 34.5
              \ny = 0723x +6.544
              \nEstimation of y when x = 32
              \ny = 0.723 (32)+ 6.544
              \n= 23.136 + 6.544 = 29.68<\/p>\n

              Question 35.
              \nFind the most probable value of y if x is 70 and the most probable value of x when y 1890 give that<\/p>\n\n\n\n\n\n
              <\/td>\nX series<\/td>\nY series<\/td>\n<\/tr>\n
              Mean<\/td>\n18<\/td>\n100<\/td>\n<\/tr>\n
              Standard deviation<\/td>\n14<\/td>\n20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

              co-efficient of correlation between x and y is 0.8
              \nAnswer:
              \nGiven:
              \nx\u0304 = 18 \u0233 = 100
              \n\u03c3x<\/sub> = 14, \u03c3y<\/sub> = 20 and \u03b3 xy<\/sub> = 0.8
              \nTo find y when x = 70 we need regression equation of y on x:
              \n\"1st
              \n= 1.1429(52)
              \ny = 59.43 + 100
              \n\u2234 y= 159.43
              \nTo find x when y = 90, we need regression equation of x on y.
              \n\"1st<\/p>\n

              Question 36.
              \nThe following data relates to marks obtained by 250 students in accountancy and statistics is 0.8. (i) Esitimate the marks obtained by a student in statistics in II PUC. Examination<\/p>\n\n\n\n\n\n
              Subject<\/td>\nArithmetic mean<\/td>\nVariance<\/td>\n<\/tr>\n
              Accountancy (x)<\/td>\n48<\/td>\n16<\/td>\n<\/tr>\n
              Statistics (y)<\/td>\n55<\/td>\n25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

              Co-efficient of correlation between mavasin accountancy and statistics is 0.8
              \n1. Estimate the marks obtained by a student instatistics who secured 50 marks in accountancy and
              \n2. Estimate the marks obtained in accountancy when marks in statistics is 65.
              \nAnswer:
              \nGiven:
              \n\\(\\bar{x}=48, \\bar{y}=55\\) \u03c3x<\/sub>2<\/sup> = 16, \u2234 \u03c3x<\/sub> = 4
              \n\u03c32<\/sup>4<\/sub> = 25 \u2234 \u03c3y<\/sub> = 5 and \u03b3 = 0.8<\/p>\n

              1. Estimation y when x = 50 regression equation of yon x : (y – \u0233) = bxy <\/sub>(x – x\u0304)
              \n\"1st
              \ny – 55 = 0.8 \\(\\frac { 5 }{ 4 }\\) (50-48)
              \ny = 1 (2) + 55
              \n\u2234 y = 2 + 55 = 57<\/p>\n

              2. Estimation g x when y = 65, use regression equation g x on y : (x – x\u0304) = bxy <\/sub>(y – \u0233)
              \n\"1st
              \nx – 48 = 0.8 \u00d7\\(\\frac { 4 }{ 5 }\\)(65-55)
              \n\u2234 x = 64+48 = 54.4<\/p>\n

              \"KSEEB<\/p>\n

              Question 37.
              \nFind two regression equations when x\u0304 = 68.2, \u0233 = 99, \\(\\frac{\\sigma_{y}}{\\sigma_{x}}\\) = 0.44 and g = 0.76. Also
              \nestimate (a) the most probable value g x when y is 12 (b) the most probable value of 4 when value g x is 16.
              \nAnswer:
              \nGiven : \\(\\frac{\\sigma_{y}}{\\sigma_{x}}\\) = 0.44, Also \\(\\frac{\\sigma_{y}}{\\sigma_{x}}\\) = \\(\\frac { 1 }{ 0.44 }\\) = 2.272
              \nThe regression equation of x on y is
              \n\"1st
              \nx – 682 = 0.76 \u00d7 2.272 (y – 9.9) = 1.7267 y – 1.7267 \u00d7 9.9
              \nx= 1.7267 y – 17.0943 + 68.2
              \n\u2234 x = 17267y + 51.1057<\/p>\n

              (a) Estimation g x when y = 12
              \nx= 1.7267 (12) + 51.1057 x = 71.8261
              \nThe regression equation of yon x is :
              \n\"1st
              \ny – 9.9 = 0.76 \u00d7 0.44 (x – 68.2) = 0.3344 x – 0.3344 \u00d7 68.2 = 0.3344 x – 22.806 + 9.9
              \ny = 0.3344x – 12.906<\/p>\n

              (b) Estimation of y when x = 16
              \ny = 0.3344 (16) – 2.906 .
              \ny = 5.3504 – 12.906 = – 7.5556<\/p>\n

              Question 38.
              \nIf the regression lines x and y are given by 2x – 3y = 0 and 47 – 5x – 8 = 0. Find the means of JC and y, also the coefficient of correlation.
              \nAnswer:
              \n2x – 3y = 0 and 4y – 5x – 8 = 0
              \nSolving both equations we get x and y. And so x\u0304,\u0233
              \n\"1st
              \nPut y = – 2.286 in 2x – 3y = 0
              \n2x – 3(-2.286) = 0
              \n2x = 6.8568
              \n\u2234 x = 3.4284
              \nx\u0304 =3.4284, \u0233 = -2.286
              \nConsider, 2x – 3y = 0. be the regression of y on x :
              \n3y = 2x + 0
              \ny = \\(\\frac { 2 }{ 3 }\\)x + 0
              \n\u2234 byx<\/sub> = \\(\\frac { 2 }{ 3 }\\)
              \nAnd 4y – 5x = 8 be the regression equation g x on J18
              \n5x = 44 – 8
              \nx = \\(\\frac { 4 }{ 5 }\\)y – \\(\\frac { 8 }{ 5 }\\)x
              \n\u2234 bxy<\/sub> = \\(\\frac { 4 }{ 5 }\\)
              \nThe coefficient of correlation is : \\(\\gamma=\\pm \\sqrt{\\mathrm{b}_{\\mathrm{xy}} \\cdot \\mathrm{b}_{\\mathrm{yx}}}\\)
              \n\\(\\gamma=\\sqrt{\\frac{4}{5} \\times \\frac{2}{3}}=0.7303\\)<\/p>\n

              Question 39.
              \nCalculate the two regression coefficients when \u03b3 = 0.9, \u03c3x<\/sub> = 10, and \u03c3y<\/sub> = 1.5
              \nAnswer:
              \nRegression coefficient g x ony : \\(\\mathrm{b}_{\\mathrm{xy}}=\\frac{\\gamma \\sigma_{\\mathrm{x}}}{\\sigma_{\\mathrm{y}}}\\)
              \n\\(b_{x y}=0.9 \\times \\frac{10}{1.5}=6\\)<\/p>\n

              Regression coefficient of yon x is :\\(\\mathrm{b}_{\\mathrm{yx}}=\\frac{\\gamma \\sigma_{\\mathrm{y}}}{\\sigma_{\\mathrm{x}}}\\)
              \n\\(b_{y x}=0.9 \\times \\frac{1.5}{10}=0.135\\)<\/p>\n

              Question 40.
              \nIf bxy<\/sub> = 0.8 and byx<\/sub> = 0.6. Find \u03b3xy<\/sub>
              \nAnswer:
              \n\\(\\gamma_{x y}=\\pm \\sqrt{b_{x y} \\cdot b_{y x}}=\\sqrt{0.8 \\times 0.6}=0.6928\\)<\/p>\n

              Question 41.
              \nFind y when the two regression coefficients are 0.6 and – 1.4
              \nAnswer:
              \n\\(\\gamma=\\pm \\sqrt{\\mathrm{b}_{\\mathrm{xy}} \\cdot \\mathrm{b}_{\\mathrm{yx}}}=\\pm \\sqrt{-0.6 \\times-1.4}\\)
              \n\u2234 \u03b3 = -0.9165 (Based on properties of regression coefficients and correlation coefficient all are negative or positive)<\/p>\n

              Question 42.
              \nA student calculated the regression co-efficients g xony as – 1.25 abd regression co\u00acefficient g yon x is -2.40 commenton his calculation.
              \nAnswer:
              \nGiven bxy<\/sub> =-1.25 and byx<\/sub> =-2.4
              \nIt is the property of the two regression coefficient is that, the geometic mean of two regression coefficients is numbericaliy equi to the coefficient of correlation. And coeficient of correlation
              \ntaks a value between + 1 and – 1. i.e., \\(\\gamma=\\pm \\sqrt{\\mathrm{b}_{\\mathrm{xy}} \\times \\mathrm{b}_{\\mathrm{yx}}}\\)
              \nHere both regression coefficients are more than 1 and so their product is also greater than 1. The students calculation is wrong.<\/p>\n

              Question 43.
              \nIf one of the regression coefficient is 1.5 and y = 0.55, find the value of other regression coefficient.
              \nAnswer:
              \nwe know that \\(\\gamma=\\pm \\sqrt{\\mathrm{b}_{\\mathrm{xy}} \\cdot \\mathrm{b}_{\\mathrm{yx}}}\\)
              \n\\(\\begin{array}{l}{0.55=\\sqrt{\\mathrm{b}_{\\mathrm{xy}} \\times 1.5}} \\\\ {(0.55)^{2}=\\mathrm{b}_{\\mathrm{xy}} \\times 1.5} \\\\ {\\frac{0.3025}{1.5}=\\mathrm{b}_{\\mathrm{xy}}}\\end{array}\\)
              \n\u2234 bxy<\/sub> =0.2017<\/p>\n

              \"KSEEB<\/p>\n","protected":false},"excerpt":{"rendered":"

              You can Download Chapter 6 Analysis of Bivariate Correlation and Regression Questions and Answers, Notes, 1st PUC Statistics Question Bank with Answers Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations. Karnataka 1st PUC Statistics Question Bank Chapter 6 Analysis of Bivariate Correlation and Regression 1st PUC …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/12405"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=12405"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/12405\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=12405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=12405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=12405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}