Question

Upload Cars04-1 Cars04-1 data and use engine size to predict the car’s city gas mileage(City MPG). Answer the questions.

I) For each additional 2.0 liter in engine size how much the MPG will change? (11.11 points)

• a. It will decrease by 0.21 mpg.
• b. It will decrease by 8.21 mpg.
• c. It will be 25.49 mpg.
• d. For car with zero horse power we expect 33.7 mpg.
• 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 city gas mileage, related or not? What is this number and why?  (11.11 points)

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

III) Given a car that has the engine size of 3.0 liters use regression analysis and all available information in there, in order to predict this car’s city gas mileage. What is your interval prediction? (11.11 points)

• a. ±4.15
• b. 33.7
• c. 21.38
• d. [17.09, 25.68]
• e. Not applicable

  EngineSize	CityMPG
  1.6	28
  1.6	28
  2.2	26
  2.2	26
  2.2	26
  2	29
  2	29
  2	26
  2	27
  2	26
  2	26
  1.7	32
  1.7	36
  1.7	32
  1.6	29
  1.6	29
  1.6	29
  2	26
  2	26
  2	26
  2.4	23
  1.6	26
  1.6	25
  1.8	24
  1.8	24
  1.8	24
  1.6	28
  1.8	28
  1.8	28
  2.2	24
  2.2	26
  2.2	26
  2.2	26
  2.2	26
  2.2	26
  1.5	32
  2.3	25
  2.3	25
  2	24
  2	22
  1.8	32
  1.8	32
  1.8	32
  1.5	35
  1.5	33
  1.5	35
  3.1	20
  3.4	21
  2.2	24
  3.5	22
  3.4	21
  2.4	22
  2.4	22
  2.4	22
  2.7	21
  2.7	21
  2.4	21
  2.4	21
  2	21
  3	20
  3	19
  2.4	26
  2.4	26
  1.7	32
  2	26
  1.4	46
  2	60
  2.7	19
  2.7	19
  2.7	20
  2.3	24
  3	20
  1.6	25
  2.5	21
  2.5	23
  2.2	24
  3.4	20
  3.8	20
  2.2	24
  3	20
  2.5	22
  2.5	21
  2.5	20
  2.4	24
  3	21
  2.4	24
  3.3	20
  1.5	59
  2	24
  1.8	24
  1.9	38
  1.8	24
  2	24
  2.4	22
  1.8	22
  2.5	20
  3.8	20
  3.8	20
  3.8	18
  3.8	20
  3.8	18
  3.5	23
  3.8	18
  3.5	18
  2.7	21
  3.5	19
  2.4	21
  2.4	22
  3.5	18
  4.6	17
  4.6	17
  3	21
  3	21
  3.5	17
  3.5	17
  3.5	18
  3.5	18
  2.5	18
  1.8	22
  3.2	19
  4.6	17
  4.6	17
  3	19
  3.5	18
  3.8	18
  3.5	21
  3.5	20
  3.5	20
  3.4	20
  3.8	20
  2.5	21
  2.5	20
  3	19
  3	21
  3	21
  3.3	20
  2.8	21
  2	24
  1.8	22
  1.9	22
  3.2	20
  1.8	23
  3	20
  3	17
  3	18
  3	20
  3	18
  2.5	20
  2.5	19
  2.5	19
  3	20
  3	20
  3	20
  2.5	19
  3.8	20
  3.8	20
  3.6	18
  3.5	18
  2.7	21
  4.6	17
  3.5	18
  3.5	19
  3	18
  3.3	20
  3	18
  3	18
  3	20
  3	20
  2.6	20
  2.6	19
  3.2	19
  3.2	20
  4.6	17
  4.6	17
  2	20
  2	20
  2.3	21
  2.3	21
  3	19
  3	21
  2.8	19
  4	18
  2.5	20
  2.3	20
  2.5	18
  2.9	20
  2.5	20
  3.5	18
  3.5	18
  3	20
  3	18
  2.7	18
  4.2	17
  4.2	17
  4.2	14
  3	19
  3	20
  4.4	18
  4.4	18
  4.4	18
  3.8	18
  4.6	18
  4.6	18
  4.6	18
  4.5	17
  4.5	17
  3	18
  4.2	18
  4.2	17
  4.2	18
  4.2	18
  4.2	17
  3	18
  4.3	18
  4.3	18
  3.9	17
  3.9	17
  4.6	17
  4.6	17
  4.6	17
  3.2	16
  5	16
  5.5	13
  3.2	20
  5	17
  3.2	19
  5	16
  4.3	18
  5	16
  2	21
  2	21
  2.4	21
  2.3	20
  2.9	19

Answer 1

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6631
R Square	0.4397
Adjusted R Square	0.4373
Standard Error	4.2997
Observations	234
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3366.4591	3366.4591	182.0938	0.0000
Residual	232	4289.1007	18.4875
Total	233	7655.5598
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	33.7066	0.9261	36.3963	0.0000	31.8820	35.5313
EngineSize	-4.1072	0.3044	-13.4942	0.0000	-4.7069	-3.5076

I) For each additional 2.0 liter in engine size how much the MPG will change?
since slope is -4.1072
for each additinal MPG will change by -4.1072 * 2 = -8.21

option B) . It will decrease by 8.21 mpg. is correct

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

III)
y^ = 33.7066 -4.1072 *x
when x = 3
y^ = 33.7066 - 4.1072*3
= 21.385

since we need prediction interval

option D) 17.09,25.68 is correct