Question 1: A furniture maker is interested in forecasting sales, and believes that there is a relationship between quarterly sales ("Y") and the number of housing starts in the same quarter one year earlier ("X1"). Also, sales of furniture are usually higher in the spring and summer than the fall and winter quarters. The maker creates a dummy variable X2 with a value corresponding to each quarter as follows:
X2 = 1 if a spring or summer quarter; and = 0 if a fall or winter quarter
The maker collects up 40 observations on sales (in 000's) and housing starts and derives the following regression equation:
Y = 125.1 + .46X1 + 25.7X2
(10.2) (6.9) (1.7)
(The t-statistic from the regression analysis is shown in parentheses below each coefficient.)
a) Interpret for someone unfamiliar with regression the meaning of the coefficient of X2, 25.7.
b) Is there a seasonal effect, based on this evidence? Why or why not?
Question 2: Baseball is a sport that generates a lot of data, which fans use to try to predict the factors that lead to successful teams. One fan compiled the team batting average and the team percentage of games won for the 14 American League teams at the end of a recent season. The presumption is that a team with a greater batting average should win more games. Supposing that these data represent a random collection of observations of these two measures, let's explore whether batting average can predict winning percentage.
a) Plot the data, and comment on what you observe.
b) Find the correlation coefficient.
c) Find the coefficient of determination R2, for this data, and interpret its meaning.
d) Find the sample regression line, and interpret the meaning of the intercept and slope coefficients of your equation.
e) Is there evidence at a 5% level of significance, that batting average can be used to predict winning percentage? Explain.