The following equation displays results of a linear regression estimated using d

Question

The following equation displays results of a linear regression estimated using data from 195 school districts in California 2. Average test Score, -645+1.79Average teachersalary The teacher salary is measured in thousands of dollars. That means that if Average teachersalary 30 then the average teacher salary in district i is $30, 000. The average teacher salary ranged from $25, 000 to S45, 000 across the districts in the sample with a sample mean of $35,993 and a sample standard deviation of $3, 191. The test score is measured on a scale that is not described in the data. However, we do know that the average test score ranged from 658 to 740 and had a sample mean of 710 and a sample standard deviation of 15. (i) Provide a clear interpretation of the slope estimate. (i) If a school district raises its teacher salaries by $10,000, what is the predicted increase in test scores? (iii) Why might the assumption the least squares assumption that E( Xi) not be valid in this case? (iv) If I took the same data, converted the X's back to dollars, rather than thousands of dollars, and then estimated the regression again, what would the new intercept and slope estimates be?

Explanation / Answer

i) slope = 1.79
it means
when average teacher salary increases by 1000 $
then on average
tes score increases by 1.79

ii)
predicted increase in test score = 1.79 * 10
= 17.9

iv)
x -> 1000x
slope will be 1/1000 of initial
then
y^ = 645+0.00179*avg teacher salary (in dollar)

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