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Using the mtcars dataset, answer the following questions: Fill in the following table: Variable Correlation with...

Using the mtcars dataset, answer the following questions:

Fill in the following table:

Variable

Correlation with mpg

cyl

-0.85216

disp

-0.84755

hp

-0.77617

drat

0.681172

wt

-0.86766

qsec

0.418684

vs

0.664039

am

0.599832

gear

0.480285

carb

-0.55093
mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21 6 160 110 3.9 2.62 16.46 0 1 4 4
Mazda RX4 Wag 21 6 160 110 3.9 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108 93 3.85 2.32 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360 175 3.15 3.44 17.02 0 0 3 2
Valiant 18.1 6 225 105 2.76 3.46 20.22 1 0 3 1
Duster 360 14.3 8 360 245 3.21 3.57 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.19 20 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.15 22.9 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.44 18.3 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.44 18.9 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.07 17.4 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.73 17.6 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.78 18 0 0 3 3
Cadillac Fleetwood 10.4 8 472 205 2.93 5.25 17.98 0 0 3 4
Lincoln Continental 10.4 8 460 215 3 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.2 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.9 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.7 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318 150 2.76 3.52 16.87 0 0 3 2
AMC Javelin 15.2 8 304 150 3.15 3.435 17.3 0 0 3 2
Camaro Z28 13.3 8 350 245 3.73 3.84 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79 66 4.08 1.935 18.9 1 1 4 1
Porsche 914-2 26 4 120.3 91 4.43 2.14 16.7 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.9 1 1 5 2
Ford Pantera L 15.8 8 351 264 4.22 3.17 14.5 0 1 5 4
Ferrari Dino 19.7 6 145 175 3.62 2.77 15.5 0 1 5 6
Maserati Bora 15 8 301 335 3.54 3.57 14.6 0 1 5 8
Volvo 142E 21.4 4 121 109 4.11 2.78 18.6 1 1 4 2
correlation -0.85216 -0.84755 -0.77617 0.681172 -0.86766 0.418684 0.664039 0.599832 0.480285 -0.55093

Which of the variables is the best predictor of mpg? Justify your answer using the correlation coefficient and a scatterplot.

Fit a regression model based on your answer to question 2. Write your model below.

Is the slope significant? Justify your answer.

Interpret the slope of your regression model.

Interpret the r2 value.

Do you believe your model is a good model for predicting mpg? Justify your answer.

Solutions

Expert Solution

Best Predictor

Since mpg has highest correlation with Weight. The correlation is neagative which indiacates that as weight increases Mileage of vehicle decreases which is obvious also.

So, weight(wt) can be considered as best predictior.

Scatter plot

From above plot it is clear that mpg and weight are highly neagtively correlatd and we can fit linear regression model to it.

Model Fitting

We need to fit model between mpg and wt . I am using Excel to fot linear regression model.

Excel Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.867659377
R Square 0.752832794
Adjusted R Square 0.744593887
Standard Error 3.045882125
Observations 32
ANOVA
df SS MS F Significance F
Regression 1 847.72525 847.72525 91.375325 0.00000000013
Residual 30 278.3219375 9.277397918
Total 31 1126.047188
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 37.28512617 1.877627337 19.85757526 0.0000000000000000008 33.45049959 41.11975275
wt -5.344471573 0.559101045 -9.559044147 0.0000000001293958701 -6.486308234 -4.202634912

Regression Model:

mpg = 37.285 - 5.3444 * wt

Slope:

Yes the slope is significant at 5 % significance level since p-value < 0.05

Interpreting slope:

The negative value of slope indicates that for each unit increase in weight mileage decreases by 5.344 units.

The decrease in mileage of vehicle with inrcease in its wieght is obvious

Interpreting R2

The R-square has value of 0.752 which indicates that 75% of variance in mpg is captured just by Weight of vehicle.

This also shows that Weight variable is good in determining the Mileage.

If we add more variables which also strong correlation with mpg like disp and cyl our R2 will increase significantly

Model

With R2 of 0.752 our model can be considered as decent. As we can see there are few outliers, so treating them will increase model efficieny little bit.

There are few other variables like disp and cyl which also has very high correlation with Mpg. Adding them while building model will increase model accuracy.

Overall, Model is good

milcah answered 1 year ago
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