The following Minitab output is regression results for heigh

The following Minitab output is regression results for height and weight of 43 men in a Penn State statistics class. Here we will define the response variable weight (y) and the explanatory variable height (x).

a)What is the equation of the estimated sample regression line?

b)What is the slope of the estimated sample regression line? Interpret!

c)If someone’s height is 70 inches, what is the predicted weight?

d)If someone in our study was 70 inches tall with a weight of 155 pounds, what is his associated residual?

e)Find the model SSE. Use this SSE value to compute the st. dev. of the regression model.

f)What is the coefficient of determination r². What does this value tell us?

g)At the 5% significance level, determine if height is useful for making weight predictions.

h)Find the 95% confidence interval for the population slope. Interpret!

i)At the 5% significance level, determine if height and weight are correlated.

j)Interpret the prediction interval for a height of 70 inches.

k)Check to verify that the model assumptions are not violated.

Solution

y= weight

x=height

a)equation of the estimated sample regression line

y= - 318 + 7 x

b)the slope of the estimated sample regression line is 7

hence Per unit change of Height will cause 7 units gain in weight

c)If x=70

y=weight=170

d)hence Residual observed-predicted=155-170= -15 pounds

e)SSE=23617

f) Coefficient of determination = 32.3%. Hence of the total variation only 32.3 % variation is explained by the given regression equation

g)

here as p vale<0.05 So we cannot use height for weight prediction at 5% level of significance level

hi) As p value<0.05 hence height and weight are not correlated

j)95% Prediction interval is (122.76,220.82)

A P.I is an interval associated with a random variable yet to be observed, with a specified probability of the random variable lying within the interval.

So the probability of observing a value within this interval is 0.

95