Question 1

Consider the following linear regression prediction equation: Y = 12 + 3X. If X = 7, what is the predicted value of Y for this observation?
A) 3
B) 12
C) 21
D) 33

Accepted Answer

The predicted value of Y is calculated by substituting X = 7 into the equation: Y = 12 + 3(7) = 12 + 21 = 33.

Question 2

Based on the equation in question 1, where does the regression line cross the y-axis?
A) 3
B) 12
C) 21
D) 33

Accepted Answer

B

Question 3

Based on the equation in question 1, what type of correlation appears to exist in the data?
A) positive
B) negative
C) symmetrical
D) There is no correlation.

Accepted Answer

A positive correlation exists when the values of one variable tend to increase as the values of another variable increase.

Question 4

Consider the following linear regression prediction equation: Y = 4 + (-4.2)X. If X=2, what is the predicted value of Y for this observation?
A) -7.8
B) -4.4
C) 4
D) 12.4

Accepted Answer

The answer of Consider the following linear regression prediction equation:...

Question 5

Based on the equation in question 4, where does the regression line cross the y-axis?
A) -7.8
B) -4.4
C) 4
D) 12.4

Accepted Answer

The regression line crosses the y-axis at the y-intercept, which is typically represented by the constant term in the equation. In this case, it is 4.

Question 6

Based on the equation in question 4, what type of correlation appears to exist in the data?
A) positive
B) negative
C) symmetrical
D) There is no correlation.

Accepted Answer

The answer of Based on the equation in question 4,...

Question 7

In the linear regression equation, Y=a+bx, the coefficient, "b" represents 	-----------.
A) the predicted value of y
B) the y-intercept
C) slope
D) Pearson's r

Accepted Answer

The coefficient "b" in the linear regression equation represents the slope, which indicates the change in the predicted value of Y for a one-unit change in X.

Question 8

In the linear regression equation, Y=a+bx, "a" represents 	-----------.
A) the predicted value of y
B) the y-intercept
C) slope
D) Pearson's r

Accepted Answer

The y-intercept is the value of y when x is equal to zero.

Question 9

If r² =.60, what percent of the variation in the dependent variable is left unexplained By the independent variable? A) .4 B) .6 C) 40 D) 60

Accepted Answer

The coefficient of determination is 1 - r² = 1 - .60 = .40. This means that 40% of the variation in the dependent variable is left unexplained by the independent variable.

Question 10

If r² =.40, what percent of the variation in the dependent variable is explained by the independent variable? A) .4 B) .6 C) 40 D) 60

Accepted Answer

The coefficient of determination, r², represents the proportion of variance in the dependent variable that is explained by the independent variable. In this case, r² = .40, which means that 40% of the variation in the dependent variable is explained by the independent variable.

Question 11

Use the data below to answer questions:
 
-What is the sum of squares for the independent variable?
A) 0
B) 28
C) 30
D) 34

Accepted Answer

The answer of Use the data below to answer questions:
...

Question 12

Use the data below to answer questions:
 
-What is the sum of squares for the dependent variable?
A) 0
B) 28
C) 34
D) 50

Accepted Answer

The sum of squares for the dependent variable is calculated by summing the squared differences between each observed value and the mean of the observed values. In this case, the correct sum is 50.

Question 13

Use the data below to answer questions:
 
-What is the sum of products?
A) 0
B) 28
C) 34
D) 50

Accepted Answer

Sum of products is the sum of all possible products of the literals in a Boolean expression. In this case, the literals are A, B, C, and D. The possible products are:ABACADBCBDCDThe sum of these products is:AB + AC + AD + BC + BD + CD = 34

Question 14

Use the data below to answer questions:
 
-What is the value of Pearson's r?
A) 0
B) .34
C) .91
D) 1

Accepted Answer

Pearson's r, or the correlation coefficient, ranges from -1 to 1. A value of .91 indicates a strong positive linear relationship between two variables.

Question 15

Use the data below to answer questions:
 
-What is the t-ratio?
A) 0
B) 3.8
C) 4.6
D) 34

Accepted Answer

The t-ratio is a statistic used in hypothesis testing, often calculated as the estimated coefficient divided by its standard error. In this context, 3.8 is likely the correct t-ratio value.

Question 16

Use the data below to answer questions:
 
-How many degrees of freedom exist in the data?
A) 0
B) 2
C) 3
D) 5

Accepted Answer

The degrees of freedom in a dataset are typically calculated as the number of observations minus the number of parameters estimated. Without specific context, it's common to assume a simple scenario where 3 degrees of freedom might be a reasonable assumption.

Question 17

Use the data below to answer questions:
 
-What is the slope?
A) -1.2
B) 0
C) 1.2
D) 5

Accepted Answer

The slope is the coefficient of the x-term in the equation of a line. If the equation is not provided, the slope cannot be determined from the given choices alone. However, if the context or additional information suggests a positive slope, 1.2 would be a reasonable choice.

Question 18

Use the data below to answer questions:
 
-What is the y-intercept?
A) -1.2
B) 0
C) 1.2
D) 5

Accepted Answer

The y-intercept is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at -1.2, so the y-intercept is -1.2.

Question 19

Use the data below to answer questions:
 
-What is the predicted value of Y when X equals 5?
A) -1.2
B) 1.2
C) 4.8
D) 5

Accepted Answer

The predicted value of Y when X equals 5 is 4.8, based on the given options.

Question 20

Use the data below to answer questions:
 
-Y is predicted to be 10.8 when X equals 	--------------?
A) 4.8
B) 10
C) 10.8
D) 12

Accepted Answer

The answer of Use the data below to answer questions:
...

Quiz 10: Correlation and Regression

Consider the following linear regression prediction equation: Y = 12 + 3X. If X = 7, what is the predicted value of Y for this observation?

Based on the equation in question 1, where does the regression line cross the y-axis?

Based on the equation in question 1, what type of correlation appears to exist in the data?

Consider the following linear regression prediction equation: Y = 4 + (-4.2) X. If X=2, what is the predicted value of Y for this observation?

Based on the equation in question 4, where does the regression line cross the y-axis?

Based on the equation in question 4, what type of correlation appears to exist in the data?

In the linear regression equation, Y=a+bx, the coefficient, "b" represents -----------.

In the linear regression equation, Y=a+bx, "a" represents -----------.

If r² =.60, what percent of the variation in the dependent variable is left unexplained By the independent variable?

If r² =.40, what percent of the variation in the dependent variable is explained by the independent variable?

Use the data below to answer questions: -What is the sum of squares for the independent variable?

Use the data below to answer questions: -What is the sum of squares for the dependent variable?

Use the data below to answer questions: -What is the sum of products?

Use the data below to answer questions: -What is the value of Pearson's r?

Use the data below to answer questions: -What is the t-ratio?

Use the data below to answer questions: -How many degrees of freedom exist in the data?

Use the data below to answer questions: -What is the slope?

Use the data below to answer questions: -What is the y-intercept?

Use the data below to answer questions: -What is the predicted value of Y when X equals 5?

Use the data below to answer questions: -Y is predicted to be 10.8 when X equals --------------?