Lecture 13

Question 1

What does the conditional standard deviation measure?

Answer 1

The variability of y values for all observations with the same X-value

Question 2

What do we assume about sigma hat when estimating it?

Answer 2

that the
standard deviation σ of the conditional distribution of Y is
identical at the various values of X

Question 3

For the line to be held as the expectation of y, what assumptions do we need?

Answer 3

1. the
   standard deviation σ of the conditional distribution of Y is
   identical at the various values of X
2. each conditional distribution is normal

Question 4

“the
standard deviation σ of the conditional distribution of Y is
identical at the various values of X” is this usually true?

Answer 4

No, we are typically violating this

Question 5

Homoschidastic form

Answer 5

standard deviation σ of the conditional distribution of Y is
identical at the various values of X

Question 6

Conditional distributions meaning

Answer 6

sets of incomes subsets of y conditional on given level of x

Question 7

“each conditional distribution is normal” assumption - what else does that entail?

Answer 7

most of the values clustered around the mean, the mean for each of those conditions being the point on the line

Question 8

“each conditional distribution is normal” does this assumption usually hold?

Answer 8

No

Question 9

Why might we want to standardize coefficients with the Pearsan correlation?

Answer 9

The slope of the prediction equation depends on the units of measurement

Question 10

Does slope of prediction equation say anything about whether association is strong or weak?

Answer 10

no - since we can make b as large or as small as we like by an
appropriate choice of units

Question 11

Two methods to say how confident we are making predictions with our line, since the y-intercept might not tell us much?

Answer 11

1. Take average of y, then see the error
2. use ordinary least squares equation and find line of best fit

Question 12

Method 1 for gauging the line’s predictive power

Answer 12

take the average of y, then see the error (how much off is each of those points off from the average); square and add up the differnces to get E1, total error related to method 1/. Uses the mean.

Question 13

Method 2 for gauging the line’s predictive power

Answer 13

use ordinary least square equation anad find line of best fit, then find error associated with that. How much squared error is there with linear regression/BEST FITTING line.

Question 14

What does the proportional reduction in error (PRE) measure?

Answer 14

Another measure of association between two quantitative
variables

Question 15

Four elements of proportional reduction in error

Answer 15

1. Rule 1 for predicting Y without using X
2. Rule 2 for predicting Y using information on X
3. A summary measure of prediction error for each rule
   -E1 for errors by rule 1
   -E2 for errors by rule 2
4. The difference in the number of errors with the two rules is
   E1 – E2. Converting…

Question 16

Basic meaning of “proportional” reduction in error?

Answer 16

how much less, reduced proportional error does method two have from method one.

Question 17

Two parts about judging the relatedness

Answer 17

The strength of association between an explanatory variable X
and a response variable Y is judged by the goodness of X as a predictor of Y

If one can predict Y much better by substituting X-values into the
prediction equation than without knowing the X-values, the
variables are strongly related