Regression

6.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

1.0000

4264225.0000

4264225.0000

22.9704

0.0007

Residual

10.0000

1856400.0000

185640.0000

Total

11.0000

6120625.0000

Coefficients

Standard Error

t Stat

P-value

Intercept

-1031.0000

658.1489

-1.5665

0.1483

Speed

1877.2727

391.6906

4.7927

0.0007

a.What is the correlation between speed and price?What does it mean?

b.What is the independent variable?

c.What is the dependent variable?

d.What is the regression equation (using the values from the output above)?

e.Is there a significant relationship between the variables?How do you know?

f.In words, what is the relationship between the two variables (i.e., strength and direction)?

g.Predict the price for a computer with a 1.9 gigahertz speed.