1 Today an article came out talking about the falling gas pr

1. Today an article came out talking about the falling gas prices and how that is likely to affect car buying - more gas guzzling SUVs and fewer fuel efficient vehicles. It got me wondering if new vehicles sales in the US were actually affected by the price of gas. Maybe lower gas prices mean greater disposable income, so people are more likely to buy a new car.

This seems reasonable, right? So I found some data. The US Bureau of Economics Analysis (BEA) had new vehicle sales, in thousands of units. I found historic gas prices in the Clean Cities Alternative Fuels Price Reports.

Here is the data from a linear regression estimate based on my question: are vehicle sales (in 1000 units) dependent on (explained by) gas prices?

a.  Using the values for the correlation coefficient and the coefficient of determination, explain to me whether or not there seems to be a relationship between gas prices and vehicle sales.  NO calculations here. Just EXPLAIN.

b. Now, at the 10% level, test whether or not there is a negative correlation between gas prices and vehicle sales.  Show work as explained in the quiz directions. Does your conclusion change at the 5% level?

c.  Write the regression equation?  What, specifically, does the slope of this equation tell me?

Solution

25.6% of the variation in vehicle sales (in 1000 units) is explained by gas prices.

r is -0.506 which is medium negative correlation.

Since the p value is 0.0648 which is less than 0.10, there is a negative correlation between the two. However at 0.05, do not reject the null and conclude that there is no correlation between the two.

sales = 1592.071 + (-121.928)gas. For every dollar increase in gas price, the number of vehicle sales fall by 121.928.