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Assignment 1

How do you interpret a coefficient of determination , equal to 0.80?

Coefficient of determination

By themselves, SSR, SSE, and SST, provide little information. However, the ratio of the regression sum of squares (SSR) to the total sum of squares (SST) measures the proportion of variation in Y that is explained by the independent variable X in the regression model. This ratio, called the coefficient of determination, , is defined in Equation (13.9).

COEFFICIENT OF DETERMAINATION

The coefficient of determination is equal to the regression sum of squares (i.e., explained variation) divided by the total sum of squares (i.e., total variation).

= = (13.9)

The coefficient of determination measures the proportion of variation in Y that is explained by the independent variable X in the regression model.

Question 2

What is the relationship between the price of crude oil and the price you pay at the pump for gasoline? The file Oil & Gas contains the price for a barrel of crude oil and a gallon of gasoline for 100 weeks ending June 1, 2009. (Data extracted from Energy information Administration, US Department of Energy).

a. Construct a scatter plot with oil on the horizontal axis and gasoline on the vertical axis.

b. Use the least-squares method to develop a simple linear regression equation to predict the price of a gallon of gasoline using the price of a barrel of crude oil as the independent variable.

c. Interpret the meaning of the slope, in this problem.

d. Plot the residual versus the time period.

e. Compute the Durbin-Watson statistic.

f. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?

g. Based on the results of (d) through (f), is there reason to question the validity of the model?

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