## Related questions with answers

A regression model to predict Y, the state burglary rate per 100,000 people for 2005 , used the following four state predictors: $X_1$= median age in 2005, $X_2$= number of 2005 bankruptcies, $X_3$= 2004 federal expenditures per capita (a leading predictor), and $X_4$=2005 high school graduation percentage. (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.

$\begin{array}{lrr} \hline \text { Predictor } & \text { Coefficient } & {\text { SE }} \\ \hline \text { Intercept } & 4,198.5808 & 799.3395 \\ \text { AgeMed } & -27.3540 & 12.5687 \\ \text { Bankrupt } & 17.4893 & 12.4033 \\ \text { FedSpend } & -0.0124 & 0.0176 \\ \text { HSGrad\% } & -29.0314 & 7.1268 \\ \hline \end{array}$

Solution

Verified**a)**

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

$Intercept: t_{\text{calc}}=\frac{4,198.5808}{799.3395}\approx 5.2526$

To calculate t-value for the AgeMed predictor divide the AgeMed coefficient by the AgeMed standard error value:

$AgeMed: t_{\text{calc}}=\frac{-27.3540}{12.5687}\approx -2.1764$

To calculate t-value for the Bankrupt predictor divide the Bankrupt coefficient by the Bankrupt standard error value:

$Bankrupt:t_{\text{calc}}=\frac{17.4893}{12.4033}\approx 1.4101$

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