Deck 10: Regression

Question 1

In calculating the regression coefficients we square the errors of prediction because

A) statisticians square everything.
B) the sum of the errors would always be 0 for a great many lines we could draw.
C) squaring makes the errors more striking.
D) little errors are more important than big errors.

Answer 1

the sum of the errors would always be 0 for a great many lines we could draw.

Question 2

The "best fitting line" is that regression line that

A) minimizes the errors of prediction.
B) minimizes each squared error of prediction.
C) minimizes the sum of squared errors of prediction.
D) hits the most points as it goes through the scatterplot.

Answer 2

minimizes the sum of squared errors of prediction.

Question 3

In the equation for a straight line used in the text, the slope is represented by

A) a
B) b
C) X
D) Y

Answer 3

b

Question 4

When we think in terms of standardized data, the slope represents

A) the change in X for a one unit change in Y .
B) the number of standard deviations Ŷ will differ for a one standard deviation difference in X .
C) the height of the regression line.
D) 0.

Question 5

When the slope of the regression line is positive, the line goes from

A) upper left to lower right.
B) lower left to upper right.
C) the line is flat.
D) It depends on the intercept.

Question 6

In the equation Ŷ  = 12.6 X + 5

A) a difference of one unit in X will lead to a 5 point difference in the prediction.
B) Ŷ will decrease as X increases.
C) the correlation is certain to be significant.
D) a difference of one unit in X will lead to a 12.6 point difference in the prediction.

Question 7

If the correlation between X and Y is negative, the slope of the regression equation must be

A) negative.
B) positive.
C) non-significant.
D) It could be either a or b.

Question 8

Suppose that you sell ice cream from a cart on the street. After you pay the ice cream supplier, the regression line that predicts your ice cream profits from the number of hours you work has a slope of 15. But the man who owns the cart charges you $5 per hour in rent. How much money will you earn per hour?

A) $15
B) $10
C) $5
D) nothing

Question 9

If we have a regression line predicting the amount of improvement in your performance as a function of the amount of tutoring you receive, an intercept of 12 would mean that

A) you need to have 12 hours of tutoring to get an A.
B) if you don't have any tutoring, the best you can do is a grade of 12.
C) even without tutoring you will improve.
D) tutoring helps.

Question 10

When we standardize paired data we

A) divide everything by the standard deviation of X .
B) convert X to a T score.
C) convert both X and Y to z scores.
D) subtract the mean from each value of X and Y .

Question 11

The notation ( Y - Ŷ ) represents

A) our best prediction.
B) the regression line.
C) the predicted value.
D) error in prediction.

Question 12

When we have considerable spread of the points about the regression line, the slope of that line will be _______ the slope of a similar line when there is less scatter.

A) less than
B) more than
C) the same as
D) more extreme than

Question 13

In the previous problem your best estimate of the intercept relating the total earning from the hours worked is

A) -10.
B) 0.
C) 10.
D) We have no idea.

Question 14

The notation Ŷ is   used instead of Y

A) to indicate that the answer is only approximate.
B) to indicate that we have an equation for a straight line.
C) to indicate that the result is a prediction.
D) because this is a mathematical equation.

Question 15

When we make a prediction using a regression equation, our prediction is _______ on X .

A) dependent
B) conditional
C) correlated
D) both a and b

Question 16

The equation for a straight line is an equation of the form

A) Y = bX × a
B) Y = bX
C) Y = bX ² + a
D) Y = bX + a

Question 17

The symbols a and b are frequently referred to as

A) regression coefficients.
B) constants.
C) slopes.
D) regression correlations.

Question 18

When we have standardized data, the slope will be denoted as

A) b
B)
C) 1.0
D) r

Question 19

When I want to make a prediction but don't have the value of X on which to base that prediction, my best estimate is

A) the value that I calculate with a regression equation.
B) the smallest value of Y.
C) the mean of Y .
D) There is no good prediction.

Question 20

In the equation for a straight line used in the text, the intercept is represented by

A) a
B) b
C) X
D) Y

Question 21

The notation SS stands for

A) simply sensational.
B) statistical significance.
C) squared sums.
D) sum of squares.

Question 22

The standard error of estimate is given by

A)
B)
C)
D) none of the above

Question 23

If you drop a pencil randomly on a scatterplot, what aspect are you changing as you rotate the pencil about the point where it crosses the Y axis?

A) the slope.
B) the intercept.
C) the correlation.
D) the residual.

Question 24

If we want to specify the percentage of the overall variability in life expectancy attributable to variability in smoking behavior, the statistic we want to look at is

A) r
B) r²
C) b
D)

Question 25

If the correlation between X and Y is significant, that tells us

A) that the slope is significant.
B) that the intercept is significant.
C) that X causes Y.
D) nothing about the regression equation.

Question 26

A significant slope means that

A) the slope is positive.
B) there is a significant relationship between X and Y in the population.
C) the slope is not equal to 0 in the population.
D) both b and c

Question 27

When we use a regression equation to make a prediction, the errors that we make are often referred to as

A) residuals.
B) predictions.
C) Ŷ
D) standard errors.

Question 28

The notation Y - Ŷ is referred to as

A) error.
B) deviation.
C) residual.
D) all of the above

Question 29

If the correlation between a body image measure and an eating disorders measure is .50, we can conclude that

A) body image has very little to do with eating disorders.
B) 50% of the variability in the eating disorders scales is associated with variability in body image.
C) one quarter of the variability in the eating disorders scores is associated with variability in body image.
D) overweight people eat too much.

Question 30

An important thing about r ² is that it represents a measure of

A) causal relationships.
B) accountable variability.
C) the correlation.
D) statistical significance.

Question 31

If data with only one predictor variable were standardized, the slope would equal

A) r
B) b
C) a
D) Ŷ

Question 32

If you want to plot the regression line, after having found the regression equation, you need to calculate Ŷ  for _______ value(s) of X .

A) all possible
B) one
C) a minimum of two
D) at least five

Question 33

If we do not know X , our measure of error in predicting Y is

A) the standard deviation of Y.
B) the standard deviation of X.
C) the standard error of estimate.
D) the standardized residual.

Question 34

If the slope is significant we know that

A) the intercept is not significant.
B) the intercept is significant.
C) there is a strong relationship between the two variables.
D) none of the above

Question 35

We can think of the standard error of estimate as

A) the standard deviation of the errors that we make when using the regression equation.
B) the standard deviation of Y.
C) the variance of the errors that we would make when using the regression equation.
D) the variance of X .

Question 36

If you drop a pencil randomly on a scatterplot, what aspect are you changing as you move the pencil vertically on the page without rotating it?

A) the slope.
B) the intercept.
C) the correlation.
D) the residual.

Question 37

The standard error of estimate is denoted by

A)
B)
C)
D) none of the above

Question 38

Which of the following does NOT belong with the rest?

A) variance attributable to
B) variance associated with
C) variance predictable from
D) variance caused by

Question 39

The regression line always passes through the point

A) 0, 0
B) ,
C) , 0
D) a, b

Question 40

If we do know X , our measure of error is

A) the standard deviation of Y.
B) the standard deviation of X.
C) the standard error of estimate.
D) the standardized residual.

Question 41

When there is only one predictor variable in a regression, beta (regression coefficient) = r (correlation coefficient).

Question 42

Regression can be used to examine both linear and curvilinear relationships.

Question 43

The regression equation can be used to estimate the value of the criterion variable based on knowing the value of the predictor variable.

Question 44

If the association between warm parenting practices and self-esteem is .50, then 75% of the variability in self-esteem is independent of warm parenting practices.

Question 45

When one refers to the degree that variable A changes as variable B changes they are referring to

A) variance.
B) regression.
C) covariance.
D) habituation.

Question 46

In a regression using standardized data, to predict health symptoms from stress, the beta = .5. This means that for every 1 point increase in stress there is half a point increase in symptoms.

Question 47

Using a regression equation to predict a value will always lead to highly accurate predictions.

Question 48

A regression line is

A) a line of covariance.
B) a correlation matrix.
C) the best fit straight line.
D) the equal to a correlation line.

Question 49

Calculate SS_error for the previous data. Explain how you did it.

Question 50

Given the following values, calculate the regression equation.

Question 51

Residual refers to the error of prediction.

Question 52

A regression analysis of hours spent exercising and ounces of weight loss had a slope of 3. We would predict that

A) for every 1 hour of exercise, a person would lose 3 ounces of weight.
B) for every ounce lost, a person has to exercise for 7 hours.
C) every hour of exercise would have no effect on weight.
D) The slope cannot be used to make predictions, you need the intercept.

Question 53

If the correlation between smoking and lung cancer is .50, smoking accounts for 50% of the variability in lung cancer.

Question 54

An example in the text hypothesized that 4% of the variability in life expectancy was accounted for by variability in smoking behavior. The values of r and r² , respectively, are equal to

A) .20 and .04.
B) .04 and .16.
C) .04 and .20.
D) More information is needed.

Question 55

Calculate the residuals for the previous data. Explain how you did it.

Question 56

The intercept of a regression line is

A) the value of Ŷ when X=0.
B) always greater than 0.
C) significant when the correlation is significant.
D) never informative.

Question 57

Regression is only appropriate for predicting a criterion variable from one predictor variable.

Question 58

Given this regression equation, Ŷ = .75 X + 5, estimate Y for the following values of X.
a. X = 0
b. X = 1
c. X = -3
d. X = 75

Question 59

In a scatterplot, an outlier is one that

A) is far to the left of the display.
B) is in the center of the display.
C) is far from the regression line.
D) is the largest value of Y .

Question 60

Regression is typically used to test cause-effect relationships.

Question 61

Given the following data, do you believe the regression equation would be a reliable way to predict values of Y. Explain your answer.

Question 62

Given the data in the previous table:
a. What is the slope of the regression line?
b. What does the value of the slope mean here?
c. Is the slope significantly different from 0?

Question 63

Write a sentence interpreting the regression data in the following table.

Dependent variable: Child Behavior Problem Score

Question 64

Answer the following questions based on the regression data in the previous table.
a. What percent of variability in behavior problems is accounted for by anger?
b. What percent of variability in behavior problems independent of anger?

Question 65

Given this regression equation,  Ŷ  = .3 X + 25, estimate the values of X given the following values of Y.
a. Y = 0
b. Y = 25
c. Y = -30

Question 66

Briefly describe the difference between the standardized beta coefficient and the unstandardized b