Chapter 17 - Prediction: Linear Regression

Question 1

What is linear regression?

Answer 1

• Plots a straight line through the scatter diagram and uses that line to predict the value of one variable from the value of the other.
• The science of linear regression provides rules for determining which is the best line for predicting one variable from the other.
• Determining the best straight line through a data set and using it to predict Y from X.

Question 2

What is slope?

Answer 2

The change in Y divided by the range of X.

Question 3

What is the intercept?

Answer 3

The general equation for a straight line is: the height of the line at any point X is equal to the slope of the line times X plus the intercept.

Question 4

p463 The equation for a straight line

Answer 4

Slope is rise/run.

Question 5

Where does the best regression line always pass through?

Answer 5

The best regression line passes through the point (X,Y), or in other words the mean of the X values and the mean of the Y values. NB: X and Y have a line above each.

Question 6

What is the error of prediction?

Answer 6

• The difference between the actual value of Y and the value predicted from X.
• It is a vertical distance between the subject’s data point and the regression line.
• Denoted by the symbol ‘e’.

Question 7

What is the least squares criterion?

Answer 7

The rule that states that the best regression line is the one that produces the smallest sum of the squared errors of prediction.

Question 8

What is the standard error of the estimate?

Answer 8

The standard deviation of the errors of prediction.

Question 9

What is homoscedasticity?

Answer 9

The assumption in regression that the size of the errors of prediction does not depend on the value of X.

Question 10

What is the coefficient of the determination?

Answer 10

The square of the Pearson correlation coefficient (r) because it measures the extent to which one variable determines the magnitude of another and therefore determines how accurate a prediction is likely to be.

Question 11

When is a prediction “good”?

Answer 11

When r is close to +1.

Question 12

When is a prediction “bad”?

Answer 12

When r is close to 0.

Question 13

What is the regression to the mean?

Answer 13

The predicted variable that generally lies closer to its mean than does the predictor variable.

Question 14

Finish this sentence… if X and Y are perfectly correlated…

Answer 14

always predict Y to be closer to the mean than is X.

Question 15

What is the personality coefficient?

Answer 15

The observations that most correlations between personality measures and behaviour are approximately .2 to .3.

Question 16

What is b?

Answer 16

b is the slope of a regression line that predicts Y from X in a sample. The slope in the corresponding population is the parameter that is called the b population.