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Exam 16: Introduction to Regression

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Question 31

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If a set of X and Y scores has r > 0,then the regression equation,= bX + a,will have a > 0.

A) True
B) False

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Question 32

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The regression equation is determined by finding the minimum value for which of the following?​

A) (X - Y) ²​
B) ​(Y -Ȳ )
C) ​(Y - ) ²
D) ​r²(Y - ) ²

E) A) and C)
F) C) and D)

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Question 33

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The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1,8.

For the regression equation,Y = X - 2,if the mean for Y is M_Y = 6,what is the mean for X?​

Find the regression equation for the following set of data.​ $\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\4 & 1 \\7 & 16 \\3 & 4 \\5 & 7 \\6 & 7\end{array}$

If the Pearson correlation between X and Y is r = 0.60,then the regression equation predicts 36% of the variance in the Y scores.

For the data below: $\begin{array} { c c } \mathrm { X } & \mathrm { Y } \\5 & 10 \\3 & 6 \\6 & 7 \\4 & 3 \\2 & 4\end{array}$ ​ a. Compute the Pearson correlation. b. Find the regression equation for predicting Y from X. c. Calculate the predicted Y for each X value, find each residual (Y - ), square each residual, and add the squared values to obtain SS_residual

For a linear regression calculated for a sample of n = 20 pairs of X and Y values,what is the value for degrees of freedom for the unpredicted portion of the Y-score variance,MS_residual?​

The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = 5.

The Pearson correlation between X₁ and Y is r = 0.50.When a second variable,X₂,is added to the regression equation,we obtain R² = 0.60.Adding the second variable increases the variability that is predicted by the regression equation for the Y scores by 36% - 25% = 11%.

The slope determines how much the Y variable changes when X is increased by one point.​

For a linear regression calculated for a sample of n = 20 pairs of X and Y values,what is the value for degrees of freedom for the predicted portion of the Y-score variance,MS_regression?​

The point defined by X = 2 and Y = -1 is located on the line defined by the equation Y = 2X - 3.

A multiple regression equation with two predictor variables is computed for a sample of n = 35 participants.The standard error of estimate for the equation would have df = 33.

If the correlation between X and Y is r = 0.00,then the regression equation,= bX + a,will have b = 0.

An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals.What are the df values for the F-ratio?​

In a multiple regression equation with two predictor variables,if b₁ is larger than b₂,then X₁ is a better predictor of the Y-score than is X₂.

A set of n = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80.How much of the variance for the Y scores is predicted by the relationship with X?​

For the linear equation Y = 2X + 4,if X increases by 1 point,how much will Y increase?​

For the regression equation,= -2X + 6,if the X value is above the mean (positive deviation) ,then what can be determined about the predicted Y value?​