Question

18.The following are measurements on length (in mm) and width (in mm) of 10 painted female turtles. Length 100 103 109 123 133 136 137 140 150 156 Width 81 86 88 94 102 100 98 105 107 115 (1)(6.5 points) Compute the least-squares regression line for predicting length from width. (Show your work!) (2)(2.5 points) Interpret the slope. (3)(2 points)Predict the length of a turtle that is 90 mm in width.

Answer 1

Sum of X = 976
Sum of Y = 1287
Mean X = 97.6
Mean Y = 128.7
Sum of squares (SS_X) = 986.4
Sum of products (SP) = 1782.8

Regression Equation = ŷ = bX + a

b = SP/SS_X = 1782.8/986.4 = 1.8074

a = M_Y - bM_X = 128.7 - (1.81*97.6) = -47.7003

ŷ = 1.8074X - 47.7003

For every increase in x there is 1.8074 increase in y

Now for x=90, ŷ = (1.8074*90) - 47.7003=114.9657=114.97