Problem
Sometimes a time trend is included in a regression as an explanatory variable, acting as a proxy for some gradual change not associated with income or price. Changing tastes might be an example. However, in the present case the addition of a time trend might give rise to a problem of multicollinearity because it will be highly correlated with the income series and perhaps also the price series. Calculate the correlations between the TIME variable in the data set, LGDPI, and the logarithm of expenditure on your category. Regress the logarithm of expenditure on your category on LGDPI, the logarithm of the relative price series, and TIME (not the logarithm of TIME). Provide an interpretation of the regression coefficients, perform appropriate statistical tests, and compare the regression results with those of the same regression without TIME.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.