Question

A sports analyst wants to exam the factors that may influence a tennis player’s chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. df SS MS F Significance F Regression 2 1.24 0.620 41.85 5.34E-09 Residual 27 0.40 0.015 Total 29 1.64 Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 0.451 0.080 5.646 5.4E-06 0.287 0.614 Double Faults −0.007 0.0024 −2.875 0.0078 −0.012 −0.002 Aces 0.015 0.003 4.65 7.8E-05 0.008 0.023 Excel shows that the 95% confidence interval for β1 is [−0.12, −0.002]. When determining whether or not Double Faults is significant at the 5% significance level, he ________.

Answer 1

Yes, because the relevant p-value is less than 0.05.

This is because,the p-value of Aces is 7.8E-05 < alpha 0.05, so we reject H0

Thus we conclude that there is significant between Wins and aces at 5% level