Consider the following data on shoulder girth and height of a group of physicall

Question

Consider the following data on shoulder girth and height of a group of physically active acults. The mean shoulder girth is 107.30 cm with a standard deviaticn of 10.31 cm. The mean height is 171.15 cm with a standard deviation of 9.42 cm. The correlation between height and shoulder girth is 0.66. 200 190 E 180 170 160 150 90 100 110 120 130 Shoulder girth (cm) (a) Write the equatlon of the regresslon line for predicting helght. Round your answers to three declmal places.) height- interpret the slope in this context. [Round your answer to three decimal places.) For each centimeter increase in shoulder girth, we would expect height to increase on average by 0603 Interpret the intercept in this context. (Round your answer to three decimal places.) People who have a shoulder girth of 0 centimeters are expected to be on average Calculate R2 of the regression line for predicting height fram shoulder girth. (Enter your answer to four cecimal places.) R2 04356 Interpret it in the context of the application. (Enter your answer to two decimal places.) Approximately 43.56 0.603 shoulder girth (b) centimeters. x centimeters tall (c) % of the variation in heights is accounted for by the model.

Explanation / Answer

Solutiona:

slope coefficient estimator=r(Sy/Sx)

=0.66*9.42/10.31

b1 =0.6030262

b1=0.603

and the constant or y intercept is

b0=ybar-b1x bar

=171.15-0.603(107.30)

=  106.4481

=106.448

y inetercept is

=106.448

regression eq is

height=106.448+0.603*shoulder girth

Solutionb:

slope=0.603 an d

y intercept is 106.448 when x=0

Solutionc:

r sq=0.66*0.66

r sq=0.4356

43.56% variation is heights is accounted ny model

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