Question

Please hurry:

What is the dependent variable? It is commonly assumed that “faster” computers cost more. To test this assumption, twelve computers were randomly selected and their processor speed (gigahertz) and price were recorded. Then a regression analysis was performed to test the linear relationship between processor speed and price. The data and the results follow.

Speed	price
2.0	$2,689
1.6	$1,229
1.6	$1,419
1.8	$2,589
2.0	$2,849
1.2	$1,349
2.0	$2,929
1.6	$1,849
2.0	$2,819
1.6	$2,669
1.0	$1,249
1.4	$1,159

SUMMARY OUTPUT

Regression Statistics

Multiple R	0.8347
R Square	0.6967
Adjusted R Square	0.6664
Standard Error	430.8596
Observations	12.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0	4264225.0	4264225.0	22.9704	0.0007
Residual	10.0	1856400.0	185640.0
Total	11.0	6120625.0
	Coefficients	Standard Error	t Stat	P-value
Intercept	-1031.000	658.1489	-1.5665	0.1483
Speed	1877.2727	391.6906	4.7927	0.0007

1) What is the dependent variable? 2) How much of the variation in price is explained by processor speed? 3) Predict the price for a computer with a 1.9 gigahertz speed. 4)Predict the price for a computer with a 2.3 gigahertz speed. 5) What is the correlation between speed and price? What does it mean? 6)What is the independent variable? 7) What is the regression equation (using the values from the output above)?  

Answer 1

1)

dependent variable=price of the computer

2) variation in price is explained by processor speed =R² =0.6967 (69.67%)

3)

Predicted price =-1031+1877.2727*1.9=2535.818

4)

predicted price =-1031+1877.2727*2.3=3286.727

5)

correlation between speed and price=0.8347 ; which is positive and near to 1 ; therefore it means that as speed increases ; price also increases,

6)

independent variable :processor speed

7)

regression equation : Price (Yhat)=-1031+1877.2727*x (processor speed)