Your textbook presented you with the following regression output: = 698.9 – 2.28
ID: 3050758 • Letter: Y
Question
Your textbook presented you with the following regression output:
= 698.9 – 2.28 × STR n = 420, R2 = 0.051, SER = 18.6
(a) How would the slope coefficient change, if you decided one day to measure testscores in 100s, i.e., a test score of 650 became 6.5? Would this have an effect on your interpretation?
(b) Do you think the regression R2 will change? Why or why not?
(c) Although Chapter 4 in your textbook did not deal with hypothesis testing, it presented you with the large sample distribution for the slope and the intercept estimator. Given the change in the units of measurement in (a), do you think that the variance of the slope estimator will change numerically? Why or why not?
Explanation / Answer
(a)
The new regression line would be NewTestScore = 6.989 - 0.0228 × STR. Hence the decimal point would
simply move two digits to the left. The interpretation remains the same, since an increase in the student-teacher
ratio by 2, say, increases the new testscore by 0.0456 points on the new testscore scale, which is 4.56 in the
original testscores.
(b)
The regression R2 should not change, since, if it did, an objective measure of fit would depend on whim (the
units of measurement). The SER will change (from 18.6 to 0.186). This is to be expected, since the TSS obviously
changes, and with the regression R2 unchanged, the SSR (and hence SER) have to adjust accordingly
(c)
Since statistical inference will depend on the ratio of the estimator and its standard error, the standard error
must change in proportion to the estimator. If this was not true, then statistical inference again would depend on the whim of the investigator.
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