Wk 13 - Regression 2

Question 1

What does the regression equation become once standardised? (x2)

Answer 1

Z-hat of y = r(Zx) = beta(Zx)

Predicted z of y = r time the z-score of x

Question 2

How do we partition variance in regression? (x1)

Which is similar to which statistical model? (x1)

Answer 2

Each person’s actual score = predicted score plus error (SSregression plus SSresidual or SSerror)
One-way independent groups ANOVA

Question 3

Explain regression to the mean (x1)

Which means that… (x1)

Answer 3

Whenever there is not a perfect correlation, the predicted value of Y is closer to the mean than the original X-value was
So, the weaker the r, the more the mean becomes a better predictor of Y

Question 4

What does the standardised regression tell us if the person is at the mean on x (z = 0)? (x3)

Answer 4

That the predicted z for y will also be zero
That y is also at the mean for y
r(Zx) = r times 0

Question 5

What does the standardised regression equation tell us if there is no correlation between x and y (r = 0)? (x3)

Answer 5

That the predicted z for y will also be zero
That y is also at the mean for y, regardless of the score on x
r(Zx) = 0 times Zx

Question 6

What does the standardised regression equation tell us if there is a perfect correlation between x and y (r = 1)? (x2)

Answer 6

That the Zy will equal Zx

r(Zx) = 1 times Zx

Question 7

If x is known, and r does not = 0, what is the best predictor of y? (x1)

Answer 7

y-hat

Question 8

If x is known, and r = 0, what is the best predictor of y? (x1)

Answer 8

The mean of y

Question 9

Why is regression to the mean an issue in applied settings? (x1)
And how to mitigate it? (x1)

Answer 9

If you give people with extreme scores a treatment, then measure them again, they will invariably have less extreme scores
Use a control group with no treatment for comparison