eCe table below: oe size, r8.5 9.0 9.0 Height /TT6:01 68.5 67.51 70.01 70.01 72.

Question

eCe table below: oe size, r8.5 9.0 9.0 Height /TT6:01 68.5 67.51 70.01 70.01 72.OTTI 5 I 09.5- 72.0 73.0 73.5 74.0 (a) Find the equation of the regression line for the data. (b) Find the correlation coefficient. (c) Describe the type of correlation and interpret the correlation in the context of the data. (d) Use the regression line to predict the value y for each of the x-values below. If the r-value is not meaningful to predict the value of y, explain why not. (A) x = size 11.5 (B) x size 15.5

Explanation / Answer

Ans:

Regression Equation(y) = a + bx

Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)

Intercept(a) = (Y - b(X)) / N

a)slope,b=(13*9539-134.5*919)/(13*1408.25-134.5^2)=1.85

y-intercept,a=(919-1.85023*134.5)/13=51.55

Regression equation:

y'=1.85x+51.55

b)

correlation coff. r=(13*9539-134.5*919)/SQRT((13*1408.25-134.5^2)*(13*65034.5-919^2))=0.915

c)positive correlation beteen shoe size and height(shoe size increases,height increases)

d)

A)when x=11.5

y'=1.85*11.5+51.55=72.825

B)x=15.5 is not meaningful to perdict y,as x=15.5 is not in the range of x values for which model is fitted.Extrapolation may cause error in perdiction.

x y xy x^2 y^2 1 8.5 66 561 72.25 4356 2 9 68.5 616.5 81 4692.25 3 9 67.5 607.5 81 4556.25 4 9.5 70 665 90.25 4900 5 10 70 700 100 4900 6 10 72 720 100 5184 7 10.5 71.5 750.75 110.25 5112.25 8 10.5 69.5 729.75 110.25 4830.25 9 11 71.5 786.5 121 5112.25 10 11 72 792 121 5184 11 11 73 803 121 5329 12 12 73.5 882 144 5402.25 13 12.5 74 925 156.25 5476 Total= 134.5 919 9539 1408.25 65034.5 slope,b= 1.850 intercept,a= 51.550 Corr. coff.= 0.915

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