Question

A sample of 20 cars was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded.

Develop a simple regression model to predict the dependent variable, MPG, using horsepower as the independent variable.

Develop a simple regression model to predict the dependent variable, MPG, using weight as the independent variable.

Using R², which of the 2 causal forecasting models, A or B, is better?

Develop a multiple regression model to predict the dependent variable, MPG, using horsepower and weight as the 2 independent variables.

Using R², how does the multiple regression model compare with each of the 2 simple regression models?

MPG (Y)	HORSEPOWER (X1)	WEIGHT (X2)
44	67	1844
44	50	1998
40	62	1752
37	69	1980
37	66	1797
34	63	2199
35	90	2404
32	99	2611
30	63	3236
28	91	2606
26	94	2580
26	88	2507
25	124	2922
22	97	2434
20	114	3248
21	102	2812
18	114	3382
18	142	3197
16	153	4380
16	139	4036

plz do it in excel.

Answer 1

1.Simple Regression Model

MPG – Dependent Variable

Horse Power – Independent Variable

The model is

Here, Y is the dependent Variable and X is the independent Variabe

	Coefficients	t Stat	P-value
Intercept	53.87238	15.73808	5.76E-12
X Variable 1	-0.26945	-7.76704	3.72E-07
Multiple R	0.877607
R Square	0.770194
Adjusted R Square	0.757427
Standard Error	4.481278
Observations	20

2.Simple Regression Model MPG – Dependent Variable Weights – Independent Variable The model is Here, Y is the dependent Variable and X is the independent Variable Coefficients t Stat P-value Intercept 57.53293 13.44194 7.96E-11 X Variable 1 -0.01079 -7.02253 1.49E-06 Multiple R 0.855923 R Square 0.732604 Adjusted R Square 0.717749 Standard Error 4.833909 Observations 20 Using R², which of the 2 causal forecasting models, A or B, is better? 3. Variables R-Squared HorsePower (as independent variable) 0.770194 Weights(as Independent variable) 0.732604 The R-squared indicates 77.01% of variations in MPG is explained by the Horse power in the regression model, whereas, 73.26% of variations in MPG is explained by the weights. Hence, the regression model using horse power as independent variable is the better model comparing with the other regression model where weights have been used as independent variable. 4.Multiple Regression model The model is Y is the dependent Variable MPG X1- is the Horse power using as independent variable X2 is the Weights using as another independent variable Coefficients t Stat P-value Intercept 57.68586 15.79907 1.36E-11 X Variable 1 -0.16567 -2.78213 0.012777 X Variable 2 -0.00505 -2.06455 0.054568 Multiple R 0.903472 R Square 0.816262 Adjusted R Square 0.794646 Standard Error 4.123182 Observations 20 5. Variables R-Squared HorsePower (as independent variable) – Model 1 0.770194 Weights(as Independent variable) Model-2 0.732604 Model 3 ( Horse power, and Weights as independent variables) 0.816262 The R-squared indicates 77.01% of variations in MPG is explained by the Horse power in the regression model, whereas, 73.26% of variations in MPG is explained by the weights. Hence, the regression model using horse power as independent variable is the better model comparing with the regression model where weights have been used as independent variable. But the multiple regression model where horsepower and weights are used as independent variables shows the R-squared value as 0.816262. It indicates that the variations in MPG is better explained by combining both the variables such as horse power and weights. It implies that 81.62% of the variations in MPG is explained by the combination of both horse power and weights. Therefore, the better model that can explain the variations more in the dependent variable is the multiple regression model.