## Question

###### Directions: There are THREE questions on this take home quiz along with one extra credit ques-...

## Answers

a)

b)

Data is:

Weight(X) Efficiency(Y) 21 34.3 23 32.3 26 29.4 29 26.9 32 24.5 34 23.1 37 21.1 41 18.6 43 17.5 50 14.2

X Values

Sum = 336n = 10

Mean = 33.6

(X - M_{x})^{2}= SS_{x}=776.4

(X - M_{x})^{2}158.76

112.36 57.76 21.16 2.56 0.16 11.56 54.76 88.36 268.96 Sum: 776.400

Y Values

Sum = 241.9

Mean = 24.19

(Y - M_{y})^{2}= SS_{y}= 389.109

(Y - M_{y})^{2}102.212

65.772

27.144

7.344

0.096

1.188

9.548

31.248

44.756

99.800

Sum: 389.109

X and Y combined

N= 10

(X - M_{x})(Y - M_{y}) =-544.94

(X - M_{x})(Y - M_{y})-127.386

-85.966

-39.596

-12.466

-0.496

-0.436

-10.506

-41.366

-62.886

-163.836

Sum: - 544.940

R Calculation

r = ∑((X - M_{y})(Y - M_{x})) / √((SS_{x})(SS_{y}))

r =-544.94 / √((776.4)(389.109))= -0.9914There exists a very strong correlation between Weights and Fuel Efficiency. The relationship is negative. If the weight increases Fuel Efficiency Decreases.

c)

Calcualting the Linear Regression equation between Weight and Fuel Efficiency using excel we get below results:

SUMMARY OUTPUTRegression Statistics Multiple R 0.991448788 R Square 0.982970698 Adjusted R Square 0.980842036 Standard Error 0.910099892 Observations 10 ANOVAdf SS MS F Significance F Regression 1 382.4827455 382.4827455 461.7785146 2.3154E-08 Residual 8 6.626254508 0.828281813 Total 9 389.109 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 47.77318393 1.134561285 42.10718676 1.11514E-10 45.15688091 50.38948694 45.15688091 50.38948694 Weight(X) -0.701880474 0.032662265 -21.48903243 2.3154E-08 -0.777199792 -0.626561156 -0.777199792 -0.626561156 Thus, equation becomes,

Fuel Efficiency(Y) = 47.77 - 0.701 * X

Now, predicting the value of efficiency using this equation we get

Weight(X)Efficiency(Y)Predicted(Y)21 34.3 33.049 23 32.3 31.647 26 29.4 29.544 29 26.9 27.441 32 24.5 25.338 34 23.1 23.936 37 21.1 21.833 41 18.6 19.029 43 17.5 17.627 50 14.2 12.72 d)

The Linear Predicted values on our scatter plot is shown below:As per HomeworkLib policy we need to solve four sub parts per question. Please post the remaining questions in another post.

Scatter Plot For weight and Fuel Efficiency 35 30 25 20 15 50 43 41 37 34 32 29 Weight in Pounds 26 23 21 Efficlency(Miles Per Gallon)We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageLinear Plot For weight and Predicted Fuel Efficiency Linear Predicted values trace1 40 30 20 10 40 20 30 50 60 Weight in Pounds Predicted Efficlency(Miles Per Gallon) 10