## Related questions with answers

A random sample of 502 Vail Resorts' guests were asked to rate their satisfaction on various attributes of their visit on a scale of 1-5 with 1= very unsatisfied and 5= very satisfied. The regression model was Y= overall satisfaction score, $X_1$= lift line wait, $X_2$= amount of ski trail grooming, $X_3$= ski patrol visibility, and $X_4$= friendliness of guest services. (a) Calculate the t statistic for each coefficient to test for $\beta_j=0$. (b) Look up the critical value of Student's t in Appendix D for a two-tailed test at $\alpha=.01$. Which coefficients differ significantly from zero? (c) Use Excel to find a p-value for each coefficient.

$\begin{array}{lcc} \hline \text { Predictor } & \text { Coefficient } & \text { SE } \\ \hline \text { Intercept } & 2.8931 & 0.3680 \\ \text { LiftWait } & 0.1542 & 0.0440 \\ \text { AmountGroomed } & 0.2495 & 0.0529 \\ \text { SkiPatroMisibility } & 0.0539 & 0.0443 \\ \text { FriendlinessHosts } & -0.1196 & 0.0623 \\ \hline \end{array}$

Solution

Verified**a)**

To calculate t-value for the Intercept predictor divide the Intercept Coefficient by the Intercept standard error value:

$Intercept: t_{\text{calc}}=\frac{2.8931}{0.3680}\approx 7.8617$

To calculate t-value for the LiftWait predictor divide the LiftWait Coefficient by the LiftWait standard error value:

$LiftWait: t_{\text{calc}}=\frac{0.1542}{0.0440}\approx 3.5045$

To calculate t-value for the AmountGroomed predictor divide the AmountGroomed Coefficient by the AmountGroomed standard error value:

$AmountGroomed:t_{\text{calc}}=\frac{0.2495}{0.0529}\approx 4.7164$

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