Question

The Department of Transportation wishes to know if states with a larger percentage of urban population have higher automobile and pickup crash death rates. In addition, it wants to know if either, the average speed on rural roads, or the percentage of rural roads that are surfaced, are related to crash death rates. Use the data file below to conduct a multiple regression analysis.

1. ANOVA table. (Conduct an hypothesis test for overall regression model using the p-value and interpret the result, calculate and interpret the coefficient of determination.)

2. Regression output. (Conduct a hypothesis test for each coefficient using the p-value and interpret the result. State the 95% confidence interval for each coefficient in the model and interpret the interval.)

3. Update the multiple regression model. (State the variables and your reasoning for including them into you model.)

4. State the result of your analysis. This should include the updated ANOVA table and the updated regression table. (What is the explaining power of your regression?)

DeathRate	PctUrbPop	AvgSpRural	PctSurf
0.209624	0.38321999	58.90000153	0.94404
0.230769	0.54711002	58.20000076	0.59767
0.203146	0.25593001	58.59999847	0.41539
0.185097	0.61374003	59.5	0.8328
0.13017	0.06938	59	0.64795
0.180638	0.18474001	55.5	0.64428
0.082581	0.0747	62.20000076	0.97966
0.131261	0.30088001	58.20000076	0.99794
0.144513	0.16197	59.90000153	0.60671
0.180491	0.43443	58.5	0.73756
0.123272	0.17836	55.20000076	0.95256
0.191646	0.83332998	56.79999924	0.52655
0.12413	0.18516999	58.29999924	0.94289
0.149746	0.34165999	58	0.96991
0.206921	0.63046998	56.90000153	0.94492
0.191667	0.56928003	57.70000076	0.74628
0.186836	0.53368998	60.20000076	0.9079
0.169821	0.36958	56.29999924	0.93895
0.13138	0.69098002	57.90000153	0.93363
0.065987	0.14443	56.79999924	0.99821
0.092739	0.03108	58.5	1
0.145772	0.18148001	59.5	0.84516
0.143769	0.368	58.40000153	0.90854
0.177977	0.73865998	61.29999924	0.97715
0.190147	0.36059001	59.29999924	0.94228
0.310992	0.75445998	58.90000153	0.5953
0.194948	0.55374998	58.5	0.81586
0.262712	0.19231001	59.70000076	0.30828
0.121921	0.50063002	57.09999847	0.80282
0.088504	0.07231	54.09999847	0.95492
0.341783	0.66131002	60.59999847	0.27209
0.077234	0.11321	57	0.95212
0.184157	0.54518002	58.90000153	0.89573
0.233282	0.87440002	59.29999924	0.66466
0.123801	0.19848999	57.09999847	0.98357
0.207531	0.39414999	56.70000076	0.61739
0.11792	0.1928	58.09999847	0.86295
0.056928	0.08565	56	0.94201
0.201705	0.51817	59	0.68717
0.235725	0.85545999	58.40000153	0.75764
0.213225	0.36893001	53.5	0.97616
0.190853	0.21827	60.09999847	0.70449
0.119701	0.2053	57.70000076	0.42227
0.086864	1	57.90000153	0.92715
0.142341	0.34096	59	0.97875
0.173938	0.28193	56.79999924	0.79592
0.206782	0.63129002	58.29999924	0.72651
0.13983	0.39667001	58.59999847	0.94195
0.550532	1	60.20000076	0.57907

Answer 1

we enter the data in excel and then goto dat > data analysis tab and select regression

we see that from the anova table the value of p is 0.00000
which is less than 0.05 , hence the model is statistically signficant

also from the gression table we see that the p value of AvgSPrural is 0.3600 , which is not less than 0.05 , hence this variable is not significant and does not contirubte towards explaining the difference

we can drop this variables from the model now

we see that from the anova table the value of p is 0.00000
which is less than 0.05 , hence the model is statistically signficant

also from the gression table we see that the p value of of all the variables are less than 0.05 , hence all the variables are signficant for the model