Question 15.5: Valley Estates Quarterly House Sales – Trend Analysis Study ......

1 Calculate the trendline equation using the sequential numbering system, x = 1, 2, 3, … Table 15.8 shows the intermediate calculations for the trendline coefficients, b_0   \text {and}  b_1, using the least squares regression formulae from Chapter 12 (Formula 12.2 for b_1 and Formula 12.3 for b_0).

The regression slope (or gradient), b_1:

b_1=\frac{16(9875)-(136)(1121)}{16(1496)-(136)^2}=\frac{5\ 544}{5\ 440} = 1.019           (using Formula 12.2)

The y-intercept, b_0:

b_0=\frac{1\ 121-1.019(136)}{16}=\frac{982.416}{16} = 61.4           (using Formula 12.3)

The regression trendline (T) is now defined by the following straight-line equation:

T = 61.4 + 1.019x

Where: x = 1 in 2008 Q1; 2 in 2008 Q2; 3 in 2008 Q3; etc.

2   Estimate trend value for the 2012 quarter 1.
To estimate the trend value of house sales for quarter 1 of 2012, the value of x that would correspond to 2012 quarter 1 is x = 17. Substitute x = 17 into the trendline equation as follows.

Trend y = 61.4 + 1.019(17) = 61.4 + 17.32 = 78.72 (rounded to 79).

Thus, the sales director of Valley Estates can be advised that the estimated trend value of house sales in quarter 1, 2012 is likely to be 79.