Question

a.​State (here) in words the specific meaning of the numerical value of the regression coefficient on engine horsepower in terms of what it measuresfor this problem. Does this coefficient make sense, according to what you would expect for it?

b.​State (here) in words the specific meaning of the numerical value of the regression coefficient on weight in terms of what it measures for this problem. (In other words, what does this number measure and how much?)

• Does this coefficient make sense, according to what you would expect for it?

c.​State (here) in words the specific meaning of the numerical value of the regression coefficient on transmission type in terms of what it measuresfor this problem. (In other words, what does this number measure and how much?)

• Does it have a practical meaning in the context of this problem? Briefly explain.

c.​State (here) in words the specific meaning of the numerical value of the “Intercept” regression coefficient in terms of what it measures for this problem. (In other words, what does this number measure and how much?)

• Does this coefficient have any practical meaningin the context of this problem? Explain.

.​a.​Overall, is this regression significant? Yes or no? Explain, including the specific statistic or statistics that were used and how they were used.

​b.​Is each individual variable coefficient significant? Yes or no for each variable. Explainfor each variable, including the specific statistic or statistics that were used and how they were used.

MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 110 90 17.7 18.1 20.3 21.5 16.9 ISS 185 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7 20.2 23.9 29.9 30.4 36.0 22.6 36.4 27.5 33.7 44.6 32.9 38.0 24.2 38.1 39.4 25.4 31.3 34.1 34.0 31.0 27.4 223 28.0 17.6 34.4 20.6 Weight 16RS 3365 3535 3445 3205 2830 3345 4360 4054 3940 2190 2044 2110 2420 2490 1455 2305 2465 3570 3155 2678 2015 1800 2015 2965 2920 2380 2850 1980 2800 2950 2560 1910 66 80 85 90 65 67 74 110 87 95 75 Transmission manual manual manual manual manual manual automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic manual manual manual manual manual manual manual manual automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic manual manual manual manual manual manual 1850 100 67 120 60 70 116 75 2615 1963 3230 1968 2070 2985 1842 1985 2395 2720 2470 2890 2025 3465 3465 3380 82 80 79 85 105

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8622
R Square	0.7435
Adjusted R Square	0.7267
Standard Error	4.2716
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	3	2432.5128	810.8376	44.4385	0.0000
Residual	46	839.3290	18.2463
Total	49	3271.8418
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	55.3878	2.4778	22.3536	0.0000	50.4002	60.3754
Horsepower	-0.1437	0.0401	-3.5853	0.0008	-0.2244	-0.0630
Weight	-0.0046	0.0016	-2.8401	0.0067	-0.0079	-0.0013
Transmission	-3.6176	1.2838	-2.8178	0.0071	-6.2018	-1.0334

(a)

The slope coefficient -0.1437 for horsepower means that for each unit of increase in horsepower, the mileage (MPG) will reduce by 0.1437.

This is intuitive because more the horsepower, the lesser should be the mileage and vice versa.

(b)

The slope coefficient -0.0046 for weight means that for each unit of increase in weight, the mileage (MPG) will reduce by 0.0046.

This is also intuitive because more the weight, more fuel is required to pull the vehicle and lesser should be the mileage and vice versa.

(c)

The slope coefficient -3.6176 for transmission means when the transmission is manual (i.e. Transmission variable = 1), the mileage (MPG) will reduce by -3.6176.

This is also intuitive because, for the manual transmission, the gear changing depends on the driver leading to a suboptimal choice of gears (sometimes) at a particular speed - this leads to poor fuel economy.

(d)

The intercept means when all the variables are set to zero value (i.e. zero weight, zero horsepower, and automatic transmission), the MPG should be 55.39.

Clearly, this does not have any real significance because zero weight, zero horsepower, and then the automatic transmission is meaningless.

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(a)

The Significance F value of the F-test in ANOVA is 0.0000. This is less than the Type-I error 0.05. So, the null hypothesis that all the slope coefficients are equal to zero is rejected. So, the model, overall, is significant at a 5% level.

(b)

Variable	P-value	Condition	Conclusion	Significant at 5%?
Horsepower	0.0008	< 0.05	Null hypothesis that the slope is zero is rejected	Yes
Weight	0.0067	< 0.05	Null hypothesis that the slope is zero is rejected	Yes
Transmission	0.0071	< 0.05	Null hypothesis that the slope is zero is rejected	Yes