Module 7 Flashcards
In a problem where we are predicting Y from X, which of the following can be considered a mean? A) Predicted value B) zX C) zY D) Error of estimate
A) Predicted value
The regression line for predicting Y from X is drawn so that which of the following is minimized? A) ∑(Ŷ - ȳ)² B) ∑(Ŷ - X)² C) ∑(Y - ȳ)² D) ∑(Y - Ŷ)²
D) ∑(Y - Ŷ)²
When the correlation is perfect, every value of \_\_\_\_ is zero A) (Y - ȳ) B) (Ŷ - ȳ) C) (Y - Ŷ) D) None of the above
C) (Y - Ŷ)
When r = .00, every value of \_\_\_\_\_ is zero. A) (Y - ȳ) B) (Ŷ - ȳ) C) (Y - Ŷ) D) None of the above
B) Ŷ - ȳ
What is the formula for intercept? A) x̄ + rȳ B) r(Sy/Sx) C) r(Sx/Sy) D) ȳ - bx̄
D) ȳ - bx̄
What is the formula for slope? A) x̄ + rȳ B) r(Sy/Sx) C) r(Sx/Sy) D) ȳ - bx̄
B) r(Sy/Sx)
In concept, the regression line is most closely related to which of the following statistical notions? A) Mean B) Median C) Standard deviation D) Variance
A) Mean
In predicting Y from X, the regression line is laid down so that the squared discrepancies between points and the line are minimized
A) In the X dimension
B) In the Y dimension
C) In a direction perpendicular to the line
D) In all of the above dimensions
B) In the Y dimension
Which terms appear in the raw score regression equation? A) x̄ B) Sy C) r D) All of the above
D) All of the above
The raw score form of the regression equation is
Ŷ = ȳ - r (Sy/Sx)x̄ + r(Sy/Sx)X
For the following data: x̄ = 100, r = +.5, ȳ = 100, Sx = 10, Sy = 10
The simplified version of the regression equation is:
A) Ŷ = 2X + 100
B) Ŷ = X + 50
C) Ŷ = 0.5X + 100
D) Ŷ = 0.5X + 50
D) Ŷ = 0.5X + 50
The amount of regression toward the mean is least when r is A) Low B) High C) Negative D) Positive
B) High
Assume a moderate positive r between father’s height and son’s adult height. For a father whose height is one standard deviation below the mean, we predict that his son’s height will be
A) More than one standard deviation below the mean
B) One standard deviation below the mean
C) Less than one standard deviation below the mean
D) At the mean
C) Less than one standard deviation below the mean
Based on midterm grades, an instructor identifies the 10 best students among his class of 100. Their average grade is A-. After the next examination he reviews their performance. He will probably find that their average grade on the second test will be A) Higher B) About the same C) Lower, but above average D) About average
C) Lower, but above average
The raw score regression equation always
A) Intersects the point where X = 0 and Y = 0
B) Intersects the point where X = x̄ and Y = ȳ
C) Slopes from lower left to upper right
D) Slopes from upper left to lower right
B) Intersects the point where X = x̄ and Y = ȳ
When r = +.50, what z score in X leads us to a predicted Y score of ȳ? A) +0.50 B) 0 C) -0.50 D) None of the above
B) 0
If the correlation coefficient is +.5 and Johnny is two standard deviations above the mean in X, what standard score position shall we predict for him in A) +2.0 B) +1.5 C) +1.0 D) None of the above
C) +1.0
x̄ = 50 and Sx = 10; ȳ = 100 and Sy = 20. If r = +.5, what value of Y do we predict for X = 60? (Hint: Think in terms of standard scores.) A) 130 B) 120 C) 110 D) 95
C) 110
When r = +1.00, what value do we predict for Y when X is 2 standard deviations below the mean?
A) 2 standard deviations below the mean
B) More than 2 standard deviations below the mean
C) Less than 2 standard deviations below the mean
D) We cannot say from the above information
A) 2 standard deviations below the mean
x̄ = 50 and Sx = 10; ȳ = 100 and Sy = 20. If r = +1.00, what value of Y do we predict for X = 40? (Hint: Think in terms of z scores.) A) 120 B) 100 C) 90 D) 80
D) 80
x̄ = 50 and Sx = 10; ȳ = 100 and Sy = 20. If r = +0, what value of Y do we predict for X = 40? A) 120 B) 100 C) 90 D) 80
B) 100
What value of r leads us to predict a Y score of ȳ, no matter what the value of X? A) 0 B) -1.00 C) +1.00 D) None of the above
A) 0
The least-squares line of regression for predicting Y from X minimizes A) Sy B) Sy and Sx C) Syx D) Sx̄
C) Syx
The standard error of prediction measures variability of
A) Predicted scores about the mean
B) Predicted scores about the regression line
C) Obtained scores about the mean
D) Obtained scores about the regression line
D) Obtained scores about the regression line
The standard error of prediction is a kind of A) Mean B) Median C) Standard deviation D) Variance
C) Standard deviation
SYX = A) S*√(1 - r²) B) Sy*√(r² - 1) C) Sx*√(1 - r²) D) Sx*√(r² - 1)
A) S*√(1 - r²)
When homoscedasticity holds, then
A) Y variability is the same for all values of X
B) r = ±0.50
C) Y variability is the same as X variability
D) Both X and Y are expressed in standard score form
A) Y variability is the same for all values of X
The method described in the text for setting error limits around predicted scores will not be unduly affected by random sampling variation if
A) Homoscedasticity holds
B) The relationship is linear
C) The sample size is at least 100
D) The standard error of prediction is used
C) The sample size is at least 100
In predicting Y from a particular value of X, we expect 68% of obtained values of Y to fall within A) ȳ ± Sy B) ȳ ± Syx C) Ŷ ± Sy D) Ŷ ± Syx
D) Ŷ ± Syx
A formula for the standard error of prediction of Y from X is A) √(∑(Y - Ŷ)² / n) A) √(∑(Ŷ - ȳ)² / n) A) √(∑(Y - ȳ)² / n) D) None of the above
A) √(∑(Y - Ŷ)² / n)
Which value of r permits the greatest accuracy of prediction? A) +.078 B) +0.27 C) -0.37 D) -0.81
D) -0.81
We are predicting scores on Y (ȳ = 50, S = 10) from scores on X. If SYX = 0, then A) r must be negative B) r must be zero C) r must be one D) None of the above
C) r must be one
Depending on the value of r, sXY may take values between: A) 0 and 1.00 B) 0 and Sy C) 0 and Sx D) Sx and Sy
B) 0 and Sy
Syx = Sy when A) Sy = Sx B) r = 0.50 C) r = 1.00 D) r = 0
D) r = 0
∑(Y - Ŷ)² will be zero when A) Sy = Sx B) r = 0.50 C) r = 1.00 D) r = 0
C) r = 1.00
∑(Y - Ŷ)² will be largest when A) The correlation is zero B) The relationship is linear C) The homoscedasticity does not hold D) The correlation is one
A) The correlation is zero
