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

a) Weight = -318 + 7.00 Height

b) The slope = 7.00. As height increases by 1 inch, the weight increases by 7 pounds.

c) Weight = -318 + 7(70) = 172 pounds

d) residual = 155 - 172 = -17

e) SSE = 23617

f) r² = 32.3%. This value tells us that 32.3% variation in weight can be explained by height.

g) p-value for height is 0.000 which is less than 0.05. This shows at the 5% significance level, height is useful for making weight predictions.