Question

a) State the Multiple Regression Equation.

b) Interpret the meaning of the slopes of this equation

c)Predict the gasoline mileage for an automobile that has a length of 195 inches and a weight of 3000 pounds.

e)Is there a significant relationship between the gasoline mileage and the two independent variables (Length and weight) at the 0.05 level of significance?

g) Interpret the meaning of the coefficient of multiple determination in this problem

i) At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

k) Construct a 95% confidence interval estimate of the population slope between gasoline mileage and weight.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.782187748
R Square	0.611817673
Adjusted R Square	0.60186428
Standard Error	2.952425134
Observations	121
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1607.421998	535.8073326	61.46825227	6.20871E-24
Residual	117	1019.867258	8.716814173
Total	120	2627.289256
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	42.43290086	8.218578926	5.163045977	1.00728E-06	26.15643651	58.70936521
Length	-0.00667189	0.036217633	-0.18421688	0.854162226	-0.07839902	0.065055222
Width	-0.03989444	0.182924039	-0.21809293	0.827736634	-0.40216590	0.322377022
Weight	-0.00487697	0.000600754	-8.11807648	5.3858E-13	-0.00606673	-0.00368720

Answer 1

(a)Gasoline_mileage(y)=42.4329-0.0067*Length-0.0399*width-0.0049*weight,

(b)there are three independent variables length,width and weight so there are 3 slope corresponding to each variables,

for length the slope is -0.0067, it means mileage will be reduced by 0.0067 units if one unit length is increased and vice-versa, provided other variables width and weight remains fixed (i.e. no change)

similarly there will be reduce in mileage by 0.0399 unit if one unit width is increased and vice-versa, provided other variables length and weight remains fixed

there will be reduce in mileage by 0.0049 unit if one unit weigth is increased and vice-versa, provided other variables length and width remains fixed

(c) answer is 26.4264

here width is not mentioned, so we assume that width is fixed so

Predicted the gasoline mileage for an automobile that has a length of 195 inches and a weight of 3000 pounds would be Gasoline_mileage(y)=42.4329-0.0067*195-0.0049*3000=26.4264

(e) there is significant relationship between gasoline mileage and weight as the p-value= 5.3858E-13 is less than typical level of significance =alpha=0.05, but length is not significant as its p-value=0.8542 is more than 0.05

(g)coefficient of determination=R-square= 0.6118, is the proportion of variability in dependent variable Gasoline_mileage(y) explained by the regression model

(i) Not, each independent variable makes a significant contribution to the regression model. only weight is significantly contributed as its p-value is less than alpha=0.05, other variables length and weight are not significantly contributed.

so we can re-analyze the data using only independent variable weight, for this raw data is needed

(k) the required 95 confidence interval for slope of weight is given as (-0.0061, -0.0037)