A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model:
E(y) = β0 + β1x,
where
y = appraised value of the house (in thousands of dollars) and
x = number of rooms. Using data collected for a sample of
n = 80 houses in East Meadow, the following results were obtained:
= 80.80 + 19.72
x
What are the properties of the least squares line,
= 80.80 + 19.72
x?
◦ It will always be a statistically useful predictor of
y.
◦ Average error of prediction is 0, and
SSE is minimum.
◦ All 80 of the sample
y-values fall on the line.
◦ It is normal, mean 0, constant variance, and independent.
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