A US consumer lobby wishes to develop a model to predict gasoline usage, as meas

Question

A US consumer lobby wishes to develop a model to predict gasoline usage, as measured by miles per gallon, based on the weight of the car in pounds. The Excel data file AUTO.xls (contained in a folder under the CML Quizzes tab) contains data on this for fifty recent models. Use Excel Data Analysis to estimate a linear model for the relationship, a 95% confidence interval for the slope coefficient and a residual plot. State all numerical answers below correct to four decimal places using the Excel output results.
1. the intercept Blank 1
2. the slope coefficient Blank 2 ,
3. the standard error of the estimate Blank 3
4. Using this model, predict the gasoline usage for a car weighing 1200 pounds. Use all decimal places in your calculation by selecting and using the values of b0 and b1 in the output generated by Excel.Blank 4
5. Does the prediction involve extrapolating the relationship? Type yes or no.Blank 5

State the

6. lower bound Blank 6 and
7. upper bound Blank 7 for the 95% confidence interval for the slope coefficient.

Gasoline usage (miles per gallon) Horsepower Weight (pounds) 43.1 48 1985 19.9 110 3365 19.2 105 3535 17.7 165 3445 18.1 139 3205 20.3 103 2830 21.5 115 3245 16.9 155 4360 15.5 142 4054 18.5 150 3940 27.2 71 3190 41.5 76 2144 46.6 65 2110 23.7 100 2420 27.2 84 2490 39.1 58 1755 28.0 88 2605 24.0 92 2865 20.2 139 3570 20.5 95 3155 28.0 90 2678 34.7 63 2215 36.1 66 1800 35.7 80 1915 20.2 85 2965 23.9 90 3420 29.9 65 2380 30.4 67 3250 36.0 74 1980 22.6 110 2800 36.4 67 2950 27.5 95 2560 33.7 75 2210 44.6 67 1850 32.9 100 2615 38.0 67 1965 24.2 120 2930 38.1 60 1968 39.4 70 2070 25.4 116 2900 31.3 75 2542 34.1 68 1985 34.0 88 2395 31.0 82 2720 27.4 80 2670 22.3 88 2890 28.0 79 2625 17.6 85 3465 34.4 65 3465 20.6 105 3380

Explanation / Answer

SUMMARY OUTPUT Regression Statistics Multiple R 0.82480863 R Square 0.680309276 Adjusted R Square 0.673649053 Standard Error 4.668104259 Observations 50 ANOVA df SS MS F Significance F Regression 1 2225.864326 2225.864326 102.1451 1.78744E-13 Residual 48 1045.977474 21.79119737 Total 49 3271.8418 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 57.7972526 2.968970159 19.46710459 2.01E-24 51.82773811 63.76676709 Weight (pounds) -0.010613111 0.001050108 -10.10668657 1.79E-13 -0.012724494 -0.008501728 Intercept 57.7972526 Slope coefficeint -0.010613111 Standard error of the estimate 4.668104259 Gasoline when car weight 1200 pounds 45.06151946 Extrapolating the relation ship? NO Lower bound 51.82773811 upper bound 63.76676709

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