The Cochrane-Orcutt method is a great preliminary methodthat estimates the parameters for the simple linear regression model with first-order autocorrelated errors given in Eq. (14.2). The attached data set gives a hypothetical time series of market share percentage and price. We expect that as price increases, fewer people buy, making the market share decrease, and vice versa. What would be great to know is how to quantify this change and correlation. This is where you come in.

Problem 1: Fit a simple linear regression model to these data. Plot the residuals versus time. Is there any indication of autocorrelation?

Problem 2: Use the Durbin-Watson test to determine if there is positive autocorrelation in the errors. What are your conclusions?

Problem 1: A simple SLR was given with a residual plot. Autocorrelation was explored.

Problem 1: Conclusions surrounding autocorrelation are correct.

Problem 2: Correct conclusions drawn with the Durbin-Watson test for autocorrelation.

Problem 3: The Cochrane-Orcutt algorithm was implemented correctly.

Problem 3: Numerical output is correct.

Problem 4: Correct and mathematically rigorous conclusions given using the regression coefficients.

Problem 5: A correct and rigorous argument for stationarity was given. Submission meets all criteria.

Month Market Share (%) Selling Price ($)

1 100 $15.93

2 98 $16.26

3 100 $15.94

4 89 $16.81

5 95 $15.67

6 87 $16.47

7 93 $15.66

8 82 $16.94

9 85 $16.60

10 83 $17.16

11 81 $17.77

12 79 $18.05

13 90 $16.78

14 77 $18.17

15 78 $17.25