Question

Use engine size to predict the car’s width. Answer the questions.

I) For each additional 3.0 liter in engine size how much the car’s width will change? (11.11 points)

• a. It will increase by 2.42 units.
• b. It will increase by 7.27 units.
• c. It will increase by 68.2 units.
• d. It will increase by 63.3 units.
• e. Not applicable.

II) After performing the regression analysis you are asked to pick one number that would best answer the question: Are these two variables, engine size and car width, related or not? What is this number and why? (11.11 points)

• a. The number is the slope and it clearly indicates the relation: For each additional liter in engine size the car’s width increases.
• b. This number is R-square and since it is not close to 1 we cannot claim that these two variables are related.
• c. The number is the P-value, which in this case is very low indicating a strong probability that the two variables are related.
• d. None of these.

III) Given a car that has engine size of 2.0 liters use regression analysis and all available information in there, in order to predict this car’s width. What is your interval prediction?   (11.11 points)

• a. [66.36, 70.09]
• b. ± 1.8
• c. 68.2
• d. 63.3
• e. Not applicable

EngineSize	Width
1.6	66
1.6	66
2.2	69
2.2	68
2.2	69
2	67
2	67
2	67
2	67
2	67
2	67
1.7	67
1.7	67
1.7	68
1.6	66
1.6	66
1.6	66
2	68
2	68
2	68
2.4	72
1.6	66
1.6	66
1.8	68
1.8	68
1.8	68
1.6	67
1.8	67
1.8	67
2.2	68
2.2	67
2.2	67
2.2	67
2.2	68
2.2	68
1.5	67
2.3	68
2.3	68
2	68
2	68
1.8	67
1.8	67
1.8	67
1.5	65
1.5	65
1.5	65
3.1	73
3.4	73
2.2	70
3.5	70
3.4	73
2.4	67
2.4	67
2.4	71
2.7	71
2.7	75
2.4	71
2.4	71
2	67
3	73
3	73
2.4	71
2.4	71
1.7	68
2	67
1.4	68
2	67
2.7	72
2.7	72
2.7	72
2.3	70
3	73
1.6	67
2.5	70
2.5	67
2.2	70
3.4	70
3.8	74
2.2	68
3	69
2.5	69
2.5	69
2.5	72
2.4	71
3	71
2.4	72
3.3	72
1.5	68
2	68
1.8	68
1.9	68
1.8	68
2	68
2.4	69
1.8	70
2.5	69
3.8	74
3.8	73
3.8	73
3.8	73
3.8	73
3.5	70
3.8	73
3.5	74
2.7	74
3.5	74
2.4	67
2.4	64
3.5	75
4.6	78
4.6	78
3	72
3	71
3.5	72
3.5	72
3.5	69
3.5	72
2.5	70
1.8	68
3.2	68
4.6	78
4.6	78
3	73
3.5	70
3.8	72
3.5	70
3.5	72
3.5	72
3.4	70
3.8	74
2.5	69
2.5	69
3	69
3	72
3	71
3.3	72
2.8	68
2	68
1.8	69
1.9	68
3.2	72
1.8	70
3	70
3	70
3	70
3	71
3	71
2.5	69
2.5	69
2.5	69
3	69
3	69
3	69
2.5	73
3.8	74
3.8	75
3.6	71
3.5	74
2.7	69
4.6	78
3.5	69
3.5	70
3	70
3.3	71
3	68
3	68
3	73
3	73
2.6	68
2.6	68
3.2	68
3.2	68
4.6	78
4.6	78
2	69
2	69
2.3	71
2.3	71
3	69
3	72
2.8	69
4	69
2.5	71
2.3	71
2.5	71
2.9	72
2.5	72
3.5	72
3.5	72
3	70
3	70
2.7	71
4.2	71
4.2	75
4.2	70
3	69
3	73
4.4	73
4.4	75
4.4	75
3.8	75
4.6	74
4.6	74
4.6	75
4.5	70
4.5	73
3	72
4.2	72
4.2	72
4.2	73
4.2	73
4.2	73
3	71
4.3	71
4.3	72
3.9	73
3.9	73
4.6	78
4.6	78
4.6	78
3.2	68
5	73
5.5	73
3.2	69
5	69
3.2	71
5	71
4.3	73
5	73
2	69
2	69
2.4	72
2.3	72
2.9	72

Answer 1

Let the regression equation be y = a + bx

y = width of the car

x = engine size.

Since the data is huge I used excel data analysis option to get the results. The results are as follows

Regression Statistics
Multiple R	0.769684
R Square	0.592413
Adjusted R Square	0.590656
Standard Error	1.863404
Observations	234

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1170.864	1170.864	337.2036	4.14E-47
Residual	232	805.5678	3.472275
Total	233	1976.432

	Coefficients	Standard Error	t Stat	P-value
Intercept	63.38357	0.401352	157.925	4.1E-238
EngineSize	2.422237	0.131908	18.36311	4.14E-47

the equation will be y = 63.38 + 2.42x

i) For each additional 3.0 liter in engine size how much the car’s width will change? (11.11 points)

It will increase by 2.42*3 units. = 7.26 units.

II) After performing the regression analysis you are asked to pick one number that would best answer the question: Are these two variables, engine size and car width, related or not? What is this number and why? (11.11 points)

• The number is the P-value, which in this case is very low indicating a strong probability that the two variables are related.

The p-value = 0.000 which states that there exists a linear relationship between the variables.

III) Given a car that has engine size of 2.0 liters use regression analysis and all available information in there, in order to predict this car’s width. What is your interval prediction?   (11.11 points)

given x = 2.0 liters mean of engine size = 2.90

for x = 2.0 => y = 63.38 + 2.42x = 63.38 + 2.42*2 = 68.22

Sxx = = 199.56

y₀ = 68.22, x₀ = 2.0

t_0.025,232 = 1.97

MSE = 3.47

by substituting all values we get 95% PI = (64.54, 71.91)

answer is not there in options correct option may be (e. Not applicable).