A regression model to predict Y, the state burglary rate per 100,000 people for

Question

A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors. X1 = median age in 2005, X2-number of 2005 bankruptcies, X3-2004 federal expenditures per capita (a leading predictor), and X4-2005 high school graduation percentage (a) Fill in the values in the table given here for a two-tailed test at = 0.01 with 42 df. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "O" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Coefficient Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% SE calc p-value 4,808.2085 799.0722 12.5026 12.3328 0.0118 7.1964 -28.944 15.3903 0.0148 28.7834 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at = 0.01 with 42 d.f? (Round your answer to 3 decimal places.) t-value (b-2) Choose the correct option Only Bankrupt differs significantly from zero Only HSGrad% differs significantly from zero Only FedSpend differs significantly from zero

Explanation / Answer

(a)

tcalc=coefficient/SE

and p-value is calcuated using ms-excel=tdist(tcalc,df,tail)=tdist(6.0172,42, 2) for intercept

(b1) two tailed critical t(0.01,42)=2.698

(b2)right choice is second Only HSGrad% differes significanly from zero

only this variable's p-value= 0.00025 is less than alpha=0.01 and

its absolute t-value=3.9997 is more than critical t=2.698

predictor Coefficient SE tcalc p-value intercept 4808.2085 799.0722 6.0172 0.00000 AgeMed -28.944 12.5026 -2.315 0.02557 Bankrupt 15.3903 12.3328 1.2479 0.21897 FedSpend -0.0148 0.0118 -1.2542 0.21669 HSGrad% -28.7834 7.1964 -3.9997 0.00025

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