DESCRIPTIVE STATISTICS MPG Length Weight Tuming orde Mean 23.29213433 1857640 44
ID: 1214312 • Letter: D
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DESCRIPTIVE STATISTICS MPG Length Weight Tuming orde Mean 23.29213433 1857640 449 3131.39 258 39 2247191 Sendard Error 0.48078 5:2 1. 40909 996 55 .43475128 0.27908 06 08 Median 18 175 Mode 20 1TMS 3450 Standard Deviation 4.535T20 472 13.29304541522.970 3076264038 0128 Sample variance 20.572T785 176700562 23498 B 68 6.9T165475 Minimum 15 149 145 Maximum 36 214 250 Sum 2073 16533 276 94 3491 Confidence Lever95.0) 0.955451 1282 000212907 110.165440556204483 CORRELATIONS MPG 1000 0.831 0906 0 727 length Weirt Turning Circle MPG Langth Weight Turning circle 1.000 0.907 0.790 1000 0720 1,000 SUMMARY OUTPUT Regress on Statistics Mut ple R 09124393 RSquare 0.832543-2 Adusted R Square 0. B2B633 428 Sandara Error 1.B88562912 Deservations gg ANO Regression Residual Total df SS MLS nificance F 315 07.240760 50e41396 140.848 8 7.04E-33 8503 1637 256 35663 a 65 8818 10.4 04494 O Coaf Plee Lowe Derg. 53.22353 897 4. 4537B8354 11501 B5768839E-20 44 36824 62.07889 0.028220 009 0.0406505106996 220804899B163 -0.052633 0.109073 -0 007309 799 0 .000913384 -8.08946156 37404E -12 -0.009205 0.005573 -0 30689 923 0 124343909 -2.457832 480015E9 B1G -0.554029 0 DE9631 1. Intercept Length Weight Turning circleExplanation / Answer
(a) MPG is miles per gallon which is the distance travelled by the car. Now the variables to be tested are length of the car, weight of the car and turning circle. The expectations suggest that:
The variables are strongly correlated individually with MPG. The correlation coefficient of values greater than 0.7 for all of the variables suggest a strong correlation.
(b) Note that all the three variables have negative sign impliying a negative relationship while we assumed that the length and turning circle should be positively related.
(c) As per the rule of thumb, if the absolute value of the t-statistic is greater than or equal to 2, then the corresponding parameter estimate is statistically different from zero. Given the values of t-statistic, the absolute values of t-statistic is greater than 2 for weight and turning circle.
Note that the P-value statistic indicates the probability that we would find the sample regression coefficient we have actually found in our sample if the null hypothesis is true. If this statistic is smaller than our chosen significance level, here 95%, we reject the hypothesis that there is no association between the relevant independent variable and the dependent variable. If it has a value (converted into a percentage) that is higher than or equal to our chosen significance level, we retain the null hypothesis.
So weight and turning circle are statistically significant and are related to the MPG.
(d)
To analyze how well the regression line fits the data, note that there hardly any difference in the value of R-Square and Adjusted R-Square, with both values being close to 0.83. However, a high value of coefficient of determination suggest that the regression line fits the data well.
The F-statistic has a value of 140.8 which is high enough. The regression is thus highly significant.
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