You have been asked to examine the relationship between two important macroecono

Question

You have been asked to examine the relationship between two important macroeconomic quantities: The change in business inventories and factory capacity utilization levels. Using the given data in attached Excel, run the regression with the change in business inventories as dependent variable and capacity utilization levels as the independent variable.

Using the regression output, find the slope of the regression line. (Round if necessary)

Using the regression output, write out the important parameters: R-squared, adjusted R-squared, the coefficients, and the coefficients' significance

Year 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 Change in inventories GDP) Capacity Utilization 0.8 77.9 83.4. 0.8 1.3 87.7 83.4 0.9 72.9 0.4 0.9 78.2 82.6 1.1 85.2 1.2 0.7 85.3 -0.3 79.5 0.9 78.3 -0.4 71.8 74.4 0.1 1.7 79.8 0.6 78.8 0.2 78.7

Explanation / Answer

Results are as follows from where we observe that

The estimated regression equation is

Change in Inventories (% GDP) = -7.336889112+ 0.09960891         Capacity Utilization (%)

Slope=0.09960891=0.10

This means corresponding to 1% increase in capactiy utilization there is on an average an increase of 0.10% in change in inventories.

R2=0.4974 and adjusted R2=0.4614 which means that capacity utilization explained 49.74% of the variability in change in inventories.

The intercept is significant with p-value=0.004<0.05

Slope is also significant with p-value=0.002<0.05.

SUMMARY OUTPUT Regression Statistics Multiple R 0.705232809 R Square 0.497353314 Adjusted R Square 0.46144998 Standard Error 0.468919487 Observations 16 ANOVA df SS MS F Significance F Regression 1 3.045978205 3.045978205 13.85256603 0.002276454 Residual 14 3.078396795 0.219885485 Total 15 6.124375 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -7.336889112 2.140731139 -3.427281912 0.004085093 -11.92830076 -2.745477462 -11.92830076 -2.745477462 Capacity Utilization (%) 0.09960891 0.026762894 3.72190355 0.002276454 0.042208211 0.157009608 0.042208211 0.157009608

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