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Notes: Before doing this assignment, do the practi...

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Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word-process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit. Problem A group of legislators wanted to look at factors that affect the number of traffic fatalities. They collected some data for 1994 from the National Transportation Safety Board on the number of fatalities for 50 states and the District of Columbia (DC), the number of licensed drivers, the number of registered vehicles, and the number of vehicle miles traveled. State Traffic Fatalities Licensed Drivers (thousands) Registered Vehicles (thousands) Vehicle Miles Traveled (millions) AL 1083 3043 3422 48956 AK 85 443 508 4150 AZ 903 2654 2980 38774 AR 610 1770 1560 24948 CA 4226 20359 23518 271943 CO 585 2620 3144 33705 CT 310 2205 2638 27138 DE 112 512 568 7025 DC 69 366 270 3448 FL 2687 10885 10132 121989 GA 1426 4666 5638 82822 HI 122 742 781 7935 ID 249 779 1062 11652 IL 1554 7548 8331 92316 IN 974 3834 4850 62108 IA 478 1921 2929 25737 KS 442 1794 1965 24678 KY 778 2498 2615 39822 LA 838 2606 3242 37430 ME 188 916 1071 12469 MD 651 3311 3543 44165 MA 440 4209 3956 46990 MI 1419 6602 7599 85183 MN 644 2668 3869 43317 MS 791 1659 2056 28548 MO 1089 3512 4179 57288 MT 202 536 967 9116 NE 271 1154 1490 15466 NV 294 987 983 13019 NH 119 878 1013 10501 NJ 761 5521 5752 60466 NM 447 1162 1472 20480 NY 1658 10444 10428 112970 NC 1431 4779 5462 71928 ND 88 443 687 6338 OH 1371 7722 9647 98200 OK 687 2363 2863 36980 OR 490 2401 2748 29453 PA 1441 8146 8557 92347 RI 63 682 728 7095 SC 847 2458 2764 37245 SD 154 512 845 7631 TN 1214 3583 5150 54524 TX 3186 12012 13287 178348 UT 342 1203 1381 18078 VT 77 435 502 6152 VA 930 4631 5593 67609 WA 638 3741 4654 47428 WV 356 1317 1375 17112 WI 712 3542 4044 50273 WY 144 354 583 6689 Source: Statistical Abstract of the United States 1996 (Reference: Pelosi and Sadifer, Doing Statistics for Business with Excel, Second Edition) (a) Copy and paste the data from this document to an Excel file. Select the Number of Traffic Fatalities as the dependent variable. Do a scatter plot between the Number of Traffic Fatalities and Number of licensed drivers (in thousands), a second scatter plot between the Number of Traffic Fatalities and the Number of Registered Vehicles (in thousands) and a third scatter plot between the Number of Traffic Fatalities and the Number of Vehicle Miles Traveled (in millions). Paste the scatter plots below and discuss the nature of the relationship based on the scatter plots. Note: Follow the instructions given in module 4 to do the scatter plots. (b) Select the Number of Traffic Fatalities as the dependent variable and the Number of licensed drivers (in thousands), the Number of Registered Vehicles (in thousands) and the Number of Vehicle Miles Traveled (in millions) as independent variables. Conduct multiple regression using Excel. Paste the output report below. Note: Follow the instructions given in module 4 to conduct simple regression. At the step where you specify the input data range, instead of selecting the data for one independent variable, select data for all the independent variables. (c) Write the equation from the regression output report. If you are using symbols in the equation for the variables, do define the symbols before using the symbols in the equation. Provide clear and complete interpretation of the coefficients b1, b2 and b3 in the equation. There is no need to interpret b0. (d) What is the value of R2 for this model? Do you think that the model does a good job of explaining the variation in the number of traffic fatalities? Why or why not? (e) Set up the hypotheses to test whether the model is significant. Is the regression model significant at 0.05 as the level of significance? What does this mean? (f) Set up the hypotheses to test for each of the regression coefficients individually and perform the test at the 0.05 level of significance. (g) What are your conclusions from the tests on individual coefficients? Do any variables need to be dropped? If so, rerun the regression and determine the final regression equation. Note: drop the variables one at a time starting with the variable with the largest p-value (least significant), rerun the regression without the data for the dropped variable, check the p-values again and continue the process until all p-values (other than for the intercept term) are less than the level of significance. (h) Compare the final equation with the first regression equation. What recommendations do you have about using the final equation? Give reasons for your answer. (i) Suppose there was a state with the following values of the independent variables: Number of Licensed Drivers (in thousands) = 3,500, Number of Registered Vehicles (in thousands) = 4,000 and Number of Vehicle Miles Traveled (in millions) = 45,000 Determine and interpret the predicted value of the number of traffic fatalities.

 

Paper#13564 | Written in 18-Jul-2015

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