Question

Help with 10-13 please? Thank you!

542 County Population (X) Elevation (X) Longitude (X) Obama% (Y) Prediction Squared Error Broomfield 57 5269 105.1 51.7 44.46 52.56 Gilpin 9141 105.5 56.7 49.44 52.65 Denver 620 5245 104.9 73.5 73.86 0.13 Lake 11580 106.3 60.4 55.50 24.01 San Juan 1 10791 107.7 52.6 56.49 15.15 Clear Creek 9 9676 105.7 51.01 10.18 Ouray 10236 1078 51.5 55.85 18.89 Sedgwick 3802 102.4 31.3 33.63 5.43 Teller 9150 1052 32.1 49.83 314.32 Summit 28 10959 106.1 61.0 55 11 34.75 Above is a table of the 2012 presidential election results for Colorado counties. I ran a regression to find out whether population (in 1000s). elevation (in feet), and longitude predict anything about the percentage of people voting for Obama. My results were be -173, pulation 0.053, belevation 0.0018, bonde - 1.95. 1. Write the regression equation, using the regression coefficients given above. P = -173 +0.053(population) +0.0018(elevation). 1.95(longitude) 2-3. Fill in the table columns for prediction and squared error. 4. Calculate the residual sum of squares. SS residual - 528.07 5. Calculate the total sum of squares of the outcome Y. Stotal = 1463.44 6. Calculate the sum of squares explained by the regression SS regression = 935.37 7. What proportion of the total variability does the regression explain? R 0.639 8-9. Convert the regression and residual sums of squares to mean squares. The degrees of freedom are dregression = m = 3 and dfresidualn -m-1 = 6. MS regression = 311.79 MSresidual = 88.01 10. Calculate the F statistic for deciding whether the regression explains meaningful variance in the outcome. 11. The critical value for F (on 3 and 6 degrees of freedom, with a 5%) is 4.76. What do you conclude? (Don't just write null or alternative.) 12. The standard error for population is 0.019. Calculate the t statistic for testing whether this regression coefficient is reliably different from zero. ta 13. The two-tailed critical value for your statistio istori - 245. Write a sentence (about counties and voting, not about hypotheses) describing what you conclude

Answer 1

(10) Compute the F statistic as follows: MSRegression F= MS Residual 311.79 88.01 = 3.54 (11) Since F-statistic (3.54) <F-critical (4.76), we fail to reject the null hypothesis. Therefore, we can conclude that there is no significant relationship between Y and X variables. (12) Compute the t statistic as follows: t= bpopulation SE (bpopulation) 0.053 0.019 = 2.79 (13) Since t-statistic (2.79) > t critical (2.45), we reject the null hypothesis. Therefore, we can conclude that population of the counties have a significant effect on the percentage of votes that Obama receives.