Question

1. Sales of major appliances vary with the new housing market: when new home sales are good, so are the sales of dishwashers, washing machines, dryers, and refrigerators. A trade association compiled the following historical data (in thousands of units) on major appliance sales (Y) and housing starts (X) Housing Starts CX) 2.0 2.5 3.2 3.6 3.3 4.0 4.2 Appliance Sales 5.0 5.5 6.0 7.0 7.2 7.7 8.4 (b) Calculate the YHATs, Residuals, and SSE (Sum of Squared Errors) and by hand.

And what is residuals, and what is sse?

Answer 1

b) YHAT = Average of Appliance Sales = (5+5.5+6+7+7.2+7.7+8.4)/7 = 46.8/7 = 6.69

Residuals = Y-average of Y

It tells how distant is each observation from the mean

So,

5-6.69 = -1.69

5.5-6.69 = 1.42

6-6.69 = 0.48

7-6.69 = 0.31

7.2-6.69 = 0.51

7.7-6.69 = 1.01

8.4-6.69 = 1.71

SSE = square of each residual = 2.86+1.42+0.48+0.1+0.26+1.02+2.92 = 9.06

SSE tells about the size of the error, bigger the number bigger is the error

Y	Residuals	SE
5	-1.69	-1.69^2=2.86
5.5	-1.19	-1.19^2=1.42
6	-0.69	-0.69^2=0.48
7	0.31	0.31^2=.10
7.2	0.51	0.51^2=0.26
7.7	1.01	1.01^2=1.02
8.4	1.71	1.71^2=2.92
	SSE	9.06