The following datashow the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.

Computer Speed Price

1 2.0 $ 2,689

2 1.6 1,229

3 1.6 1,419

4 1.8 2,589

5 2.0 2,849

6 1.2 1,349

7 2.0 2,929

8 1.6 1,849

9 2.0 2,819

10 1.6 2,669

11 1.0 1,249

12 1.4 1,159

A. Develop a linear equation that can be used to describe how the price depends on the processor speed.

B. Based on your regression equation, is there one machine that seems particularly over-or-underpriced.

C. Compute the correlationcoefficient between the two variables. At the .05 significance level conduct a test of hypothesis to determine if the population correlation could be greater than zero

2. What is correlation? Does correlation prove causation? Why or why not? Explain and provide examples to support your explanation.

Dear Student,

The solutions are outlined below.

1. The following data show the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.

Computer Speed Price

1 2.0 $ 2,689

2 1.6 1,229

3 1.6 1,419

4 1.8 2,589

5 2.0 2,849

6 1.2 1,349

7 2.0 2,929

8 1.6 1,849

9 2.0 2,819

10 1.6 2,669

11 1.0 1,249

12 1.4 1,159

A. Develop a linear equation that can be used to describe how the price depends on the processor speed.

Let the relationship between speed and price be modeled by:

Price = A x Speed + B where A and B are some constants.

We can find A and B by using simple linear regression by the method of least squares.

Let sum of all speeds be spsum = 2 + 1.6 + 1.6 + 1.8 + 2.0 + 1.2 + 2.0 + 1.6 + 2.0 + 1.6 + 1.0 + 1.4 = 19.8

Let sum of all prices be prsum = 2689 + 1229 + 1419 + 2589 + 2849 + 1349 + 2929 + 1849 + 2819 + 2669 + 1249 + 1159 = 24798

Let the sum of the squares of all speeds be sqsum = 2^2 + 1.6^2 + …………1.4^2 = 33.88 where ^ means to the power of.

Let the sum of the squares of all prices be psqsum = 2689^2 + 1229^2 + …..1159^2 = 57365692

Sum of the products of price and speed is spprsum = 2×2689 + 1.6×1229 + 1.8×1419 + …

The solution examines linear equations for price and processor speeds.The correlation is determined.