Coleman has purchased a machine that will launch a tennis ball into the air for his dog Lulu to go fetch and bring back to him. He can adjust the angle that the ball is launched to achieve different distances of travel for the ball.

Below is a table of the results of an experiment launching the ball at ten different angles (degrees) and recording

the distances traveled (feet).

Angle (x) 20 25 30 35 40 45 50 55 60 65

Distance (y) 176215248 269 282 280 270 244 212 175

a. (2 points) Construct a scatterplot of the data.

b. (2 points) Coleman thinks that a quadratic regression model would fit this data better than a linear

regression model. Do you agree? Use an interpretation of the scatterplot to explain your answer.

c. (3 points) Assuming that a quadratic regression model is appropriate, obtain the equation of the estimated

regression line.

d. (2 points) Based upon the coefficient of determination, is this model a good fit to the data? Explain.

e. (3 points) Check the regression assumptions using a normal probability plot of the residuals and a plot

of the unstandardized predicted values versus the studentized residuals. [Hint: Be sure to interpret

each of the plots with respect to the relevant assumption(s).]

f. (2 points) Obtain a 90% confidence interval to estimate the distance the ball will travel on average if Coleman sets the angle to 5 degrees. Explain why these results don't make sense and what might be the reason behind obtaining such results.