Question

Upload Cars04-1 data and use cylinder numbers to predict the car’s horse power. Answer the questions.

I) For an additional 2.0 cylinders how much the car’s horse power will change? (10 points) a. It will increase by 150 units. b. It will increase by 36.5 units. c. It will increase by 73.2 units. d. It will decrease by 2.01 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, number of cylinders and horse power, related or not? What is this number and why? (10 points) a. The number is the slope and it clearly indicates the relation: For each additional cylinder the horse power 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 4.0 cylinders use regression analysis and all available information in there, in order to predict this car’s horse power. What is your interval prediction? (10 points) a. [109.5, 179.1] b. 170.6 ± 34.7 c. 144.3 d. [178.6, 185.4] e. Not applicable

Answer 1

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.840541555
R Square	0.706510105
Adjusted R Square	0.705245062
Standard Error	34.7650477
Observations	234
ANOVA
	df	SS	MS	F	Significance F
Regression	1	674992.3782	674992.3782	558.4871817	1.08195E-63
Residual	232	280397.1817	1208.608542
Total	233	955389.5598
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.018282403	8.837117333	-0.228386965	0.819546598	-19.42954157	15.39298
Cylinders	36.58038581	1.547895639	23.63233339	1.08195E-63	33.53065691	39.63011

i)

for additional 2 cylinder

36.6 * 2 = 73.2

c. It will increase by 73.2 units.

ii)

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

iii)

y^ = -2.01828 + 36.580386 *x

x = 4

y^ = 144.3032

option A) is correct