Question

1. Write the reqression equation
2. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4. Interpret the coefficient for the independent variable.
5. What percentage of the observed variation in highway fuel efficiency that is explained by the model?
6. f.Predict the highway fuel efficiency of a vehicle with 6 gears

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.40519
R Square	0.164179
Adjusted R Square	0.158531
Standard Error	5.086625
Observations	150
ANOVA
	df	SS	MS	F	Significance F
Regression	1	752.1843	752.1843	29.07132	2.69862E-07
Residual	148	3829.316	25.87375
Total	149	4581.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	37.21006	1.812045	20.53485	3.66E-45	33.6292408	40.79089	33.62924	40.79089
# Gears	-1.36117	0.252453	-5.39178	2.7E-07	-1.860051705	-0.86229	-1.86005	-0.86229

Answer 1

1)

Regression model

  highway fuel efficiency of a vehicle = 37.21006 - 1.36117 * Gears

2)

this model is statistical significant at alpha = 0.05 , becouse Significance F < alpha.

3)

Gears are statistical significant at alpha = 0.05 level and also intercept are significant at alpha =0.05.Both p-value are less than 0.05.

4)

The predicat  highway fuel efficiency of a vehicle to increase by 37.21006 as per one unit of  highway fuel efficiency of a vehicle.

The predicat  highway fuel efficiency of a vehicle to Gears decrease by -1.36117 as per one unit of  highway fuel efficiency of a vehicle.

5)

R-Square = 0.164179

16.42 % of the observed variation in highway fuel efficiency that is explained by the model.It's mean's that the our model is not good fit for given data .

6)

Given value Gears = 6

Regression model :

highway fuel efficiency of a vehicle = 37.21006 - 1.36117 * Gears

highway fuel efficiency of a vehicle = 37.21006 - 1.36117 * 6

highway fuel efficiency of a vehicle = 29.04304

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Note1; Our fit regression model is not good for given data please check the regression assumptions of regression equation. like, dependent variable are follow normal distribution, if not follow not normal distribution then used the log transformation.

a) outliear present it our data then remove it used the following formula.

mean+3*sigma

b) Remove the multicollinearity using the VIF = 1/(1- R-square ).

c) Also check the heteroscedasticity remove . used to if independent variable of each other  are high correlation > 0.7 then remove it.

all step check it then fit Regression model for given data set. then improve our model accuracy.

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NOTE 2 : :If you want any additional information then comment please below i will provide ans.