# Question

Based on data on 2,679 high school basketball players, the following model was fitted:

y = b0 + b1x1 + b2x2 + g + b9x9 + e

where

y = minutes played in season

x1 = field@goal percentage

x2 = free@throw percentage

x3 = rebounds per minute

x4 = points per minute

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 parentheses) were as follows:

The coefficient of determination was as follows:

R2 = 0.5239

a. Find and interpret a 90% confidence interval for β6.

b. Find and interpret a 99% confidence interval for β7.

c. Test, against the alternative that it is negative, the null hypothesis that β8 is 0. Interpret your result.

d. Test, against the alternative that it is positive, the null hypothesis that β9 is 0. Interpret your result.

e. Interpret the coefficient of determination.

f. Find and interpret the coefficient of multiple correlation.

y = b0 + b1x1 + b2x2 + g + b9x9 + e

where

y = minutes played in season

x1 = field@goal percentage

x2 = free@throw percentage

x3 = rebounds per minute

x4 = points per minute

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 parentheses) were as follows:

The coefficient of determination was as follows:

R2 = 0.5239

a. Find and interpret a 90% confidence interval for β6.

b. Find and interpret a 99% confidence interval for β7.

c. Test, against the alternative that it is negative, the null hypothesis that β8 is 0. Interpret your result.

d. Test, against the alternative that it is positive, the null hypothesis that β9 is 0. Interpret your result.

e. Interpret the coefficient of determination.

f. Find and interpret the coefficient of multiple correlation.

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