Regression 3 r= 0.771418 Accidents per 1000 miles(x) Deaths (y) 147.63 16.17 246

Question

Regression 3 r= 0.771418 Accidents per 1000 miles(x) Deaths (y) 147.63 16.17 246.05 63 344.47 58.8 393.68 37.8 492.1 78.75 541.31 35.7 590.52 42 590.52 117.6 639.73 92.82 738.15 52.5 738.15 73.5 787.36 127.68 885.78 129.36 934.99 116.55 984.2 151.2 SUMMARY OUTPUT Regression Statistics Multiple R 0.771418118 R Square 0.595085912 Adjusted R Square 0.563938674 Standard Error 27.04927483 Observations 15 ANOVA df SS MS F Significance F Regression 1 13978.84814 13978.85 19.10558 0.000757079 Residual 13 9511.622495 731.6633 Total 14 23490.47064 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept 3.010208024 18.85480177 0.159652 0.875609 -37.72311474 43.74353 -53.785656 59.80607183 Accidents per 1000 miles(x) 0.126816403 0.029013182 4.370993 0.000757 0.064137234 0.189496 0.0394207 0.214212111 RESIDUAL OUTPUT Observation Predicted Deaths (y) Residuals 1 21.73211367 -5.56211367 2 34.2133841 28.7866159 3 46.69465453 12.10534547 4 52.93528975 -15.1352897 5 65.41656018 13.33343982 6 71.65719539 -35.9571954 7 77.89783061 -35.8978306 8 77.89783061 39.70216939 9 84.13846582 8.681534175 10 96.61973626 -44.1197363 11 96.61973626 -23.1197363 12 102.8603715 24.81962853 13 115.3416419 14.0183581 14 121.5822771 -5.03227712 15 127.8229123 23.37708767 2. Using the regression analysis, answer the following questions: a. Is the correlation coefficient significant? b. What is the coefficient of determination? c. What does this coefficient tell you? d. What is the slope of the regression line? e. What is the y intercept? f. Give the slope/intercept equation for this data. g. What information does the Residuals Plot provide? Regression 3 r= 0.771418 Accidents per 1000 miles(x) Deaths (y) 147.63 16.17 246.05 63 344.47 58.8 393.68 37.8 492.1 78.75 541.31 35.7 590.52 42 590.52 117.6 639.73 92.82 738.15 52.5 738.15 73.5 787.36 127.68 885.78 129.36 934.99 116.55 984.2 151.2 SUMMARY OUTPUT Regression Statistics Multiple R 0.771418118 R Square 0.595085912 Adjusted R Square 0.563938674 Standard Error 27.04927483 Observations 15 ANOVA df SS MS F Significance F Regression 1 13978.84814 13978.85 19.10558 0.000757079 Residual 13 9511.622495 731.6633 Total 14 23490.47064 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept 3.010208024 18.85480177 0.159652 0.875609 -37.72311474 43.74353 -53.785656 59.80607183 Accidents per 1000 miles(x) 0.126816403 0.029013182 4.370993 0.000757 0.064137234 0.189496 0.0394207 0.214212111 RESIDUAL OUTPUT Observation Predicted Deaths (y) Residuals 1 21.73211367 -5.56211367 2 34.2133841 28.7866159 3 46.69465453 12.10534547 4 52.93528975 -15.1352897 5 65.41656018 13.33343982 6 71.65719539 -35.9571954 7 77.89783061 -35.8978306 8 77.89783061 39.70216939 9 84.13846582 8.681534175 10 96.61973626 -44.1197363 11 96.61973626 -23.1197363 12 102.8603715 24.81962853 13 115.3416419 14.0183581 14 121.5822771 -5.03227712 15 127.8229123 23.37708767 2. Using the regression analysis, answer the following questions: a. Is the correlation coefficient significant? b. What is the coefficient of determination? c. What does this coefficient tell you? d. What is the slope of the regression line? e. What is the y intercept? f. Give the slope/intercept equation for this data. g. What information does the Residuals Plot provide?

Explanation / Answer

a)

The p-valueof t test of slope is 0.0008. SInce p-value is less than 0.05 so it is significant.

b)

The r-sqaure is knonw as coeffcient of determination. The r-sqaure is 0.5951.

c)

59.51% of variaiton in dependnet variable is explained by independent variable.

d)

The slope is : 0.1268

e)

The y-intercept is : 3.0102

f)

The regression equation is; y' = 3.0102 + 0.1268x

g)

Need residual plot for this part

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