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. Based on this information, the forecast value of the average mortgage interest rate in 2018 would be ______ percent. Express your answer without rounding.
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. Based on this information, the forecast value of the average mortgage interest rate in 2018 would be ______ percent. Express your answer without rounding.
Solution
To forecast the average mortgage interest rate in 2018, we first need to determine the value of X for 2018. The data starts from 1987, so we subtract 1987 from 2018 to get X = 31.
The estimated equation given is Y = 10.50 - 0.24X. We can substitute X = 31 into this equation to forecast the average mortgage interest rate in 2018.
Y = 10.50 - 0.24(31) = 10.50 - 7.44 = 3.06
So, the forecast value of the average mortgage interest rate in 2018 would be 3.06 percent.
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