Based on data on 2,679 high school basketball players, the following model was fitted:
y = B- + B1X1 + B2X2 + ..... + B9X9 + e
where,
y = minutes played in season
x1 = field-goal percentage
x2 = free-throw percentage
x3 = rebounds per minute
x4 = points per game
x5 = fouls per minute
x6 = steals per minute
x7 = blocked shots per minute
x8 = turnovers per minute
x9 = assists per minute
The least squares parameter estimates (with standard errors in parenthesis) were as follows:
b0 = 358.848 (44.695), b1 = 0.6742 (0.0639), b2 = 0.2855 (0.0388)
b3 = 303.81 (77.73), b4 = 504.95 (43.26), b5 = -3923.5 (120.6)
b6 = 480.04 (224.9), b7 = 1350.3 (212.3) b8 = -891.67 (180.87)
b9 = 722.95 (110.98)
The coefficient of determination was as follows:
R^2 = 0.5239
a. Find and interpret a 90-% confidence interval for B6
b. Find and interpret a 99% confidence interval for B7
c. test, against the alternative that it is negative, the null hypothesis that B8 = 0. Interpret your result/
d. Test, against the alternative that it is positive, the null hypothesis that B9 is 0. Interpret your result.
e. Interpret the coefficient of determination.
f. Find and interpret the coefficient of multiple correlation.