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The level at which commercial lending institutions set mortgage interest rates has a significant effect on the volume of buying, selling, and construction of residential and commercial real estate. A researcher collected data on annual average mortgage interest rates (for conventional, fixed-rate, 30-year loans) for the period 1987–2010, and run a linear trend regression of Y (average mortgage interest rate expressed as a percentage) on X (time period, X = 0, 1, 2......, n). The estimated equation has a Y-intercept of 10.50 and a slope of -0.24. The slope can be interpreted as a. The average mortgage interest rate set by commercial lending institutes is predicted to fall by 0.24% per year, on average. b. The average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.26% per year, on average. c. The average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.74% per year, on average. d. TThe average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.50% per year, on average.

Question

The level at which commercial lending institutions set mortgage interest rates has a significant effect on the volume of buying, selling, and construction of residential and commercial real estate. A researcher collected data on annual average mortgage interest rates (for conventional, fixed-rate, 30-year loans) for the period 1987–2010, and run a linear trend regression of Y (average mortgage interest rate expressed as a percentage) on X (time period, X = 0, 1, 2......, n). The estimated equation has a Y-intercept of 10.50 and a slope of -0.24. The slope can be interpreted as a. The average mortgage interest rate set by commercial lending institutes is predicted to fall by 0.24% per year, on average. b. The average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.26% per year, on average. c. The average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.74% per year, on average. d. TThe average mortgage interest rate set by commercial lending institutes is predicted to rise by 10.50% per year, on average.

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Solution

The correct answer is:

a. The average mortgage interest rate set by commercial lending institutes is predicted to fall by 0.24% per year, on average.

The slope of a linear regression line represents the rate of change in the dependent variable (Y) for each one-unit change in the independent variable (X). In this case, the slope of -0.24 indicates that for each one-unit increase in time (each year), the average mortgage interest rate is predicted to decrease by 0.24%.

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