Question 1

The equation of a regression line is  . What is the intercept of this line?
A) -4.6
B) 3.2
C) 4.6
D) 0

Accepted Answer

The intercept of a regression line represents the value of the y-variable when the x-variable is equal to zero. Since we don't have any information about the x-variable, we can't determine the intercept exactly. However, we do know that the intercept will not be negative, as e to any power is always positive. Therefore, the only possible choice for the intercept is 4.6, which is answer choice C.

Question 2

Using a regression line of  , a value of x = 3.6 would result in a predicted value of  .

Accepted Answer

The question does not provide information on the slope and intercept of the regression line, which are necessary to calculate the predicted value. Therefore, it is not possible to determine if a value of x = 3.6 would result in a predicted value.

Question 3

A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded.
a. Draw a scatter plot.
b. Determine the regression line equation and plot the regression line
on the scatter plot.

Accepted Answer

The answer of A psychologist wants to determine if there...

Question 4

A correlation coefficient r was calculated to be 0.830. The coefficient of nondetermination would be 0.170.

Accepted Answer

The coefficient of nondetermination is calculated by subtracting the square of the correlation coefficient from 1. Therefore, in this case it would be: 1 - (0.83)^2 = 0.3121, not 0.170.

Question 5

A regression line was calculated as  . The slope of this line is -3.2.

Accepted Answer

The statement indicates that a regression line was calculated and its identifier is given as "11eaa984_72e6_3c5d_97c0_21c12f020752_TB1705_00". The slope of this line is given as -3.2. Since the statement does not raise any doubt regarding the validity of the calculation or the accuracy of the reported slope, we can assume that the slope of the regression line is indeed -3.2. Therefore, the answer is A)True.

Question 6

If the correlation coefficient is 0.790, what is the explained variation?
A) 37.6%
B) 62.4%
C) 79%
D) 21%

Accepted Answer

The correlation coefficient squared (r^2) gives the proportion of variance explained in one variable by the other. Thus, 0.790^2 = 0.624, which is 62.4%. This means that 62.4% of the variation in one variable can be explained by the other variable.

Question 7

If the equation for the regression line is y' = 7x - 9, then a value of x = 2 will result in a predicted value for y of
A) 16
B) 25
C) 23
D) 5

Accepted Answer

The answer of If the equation for the regression line...

Question 8

The formula for the coefficient of nondetermination is 1.00 - r² .

Accepted Answer

The coefficient of nondetermination is the proportion of variance not explained by the model, calculated as 1 minus the coefficient of determination (r²).

Question 9

If the equation for the regression line is y' = -4x + 3, then the slope of this line is
A) 6
B) 3
C) -1
D) -4

Accepted Answer

The slope of the regression line is the coefficient of x, which is -4 in this case. Therefore, the answer is D.

Question 10

The variation due to chance, found by the formula __________, is called the unexplained variation.

Accepted Answer

The answer of The variation due to chance, found by...

Question 11

A regression line can be used to show trends in data.

Accepted Answer

A regression line is a straight line that shows the general pattern of the relationship between two variables, such as the correlation between height and weight. It can help to identify trends and make predictions about future data points.

Question 12

If the equation for the regression line is y' = 8x + 4, then a value of x = -3 will result in a predicted value for y of
A) 4
B) -4
C) -20
D) 8

Accepted Answer

Substituting x = -3 in the equation for the regression line, we get:
y' = 8(-3) + 4
y' = -24 + 4
y' = -20
Therefore, the predicted value of y when x = -3 is -20.

Question 13

If the correlation coefficient is 0.930, what is the unexplained variation?
A) 7%
B) 93%
C) 13.5%
D) 86.5%

Accepted Answer

The answer of If the correlation coefficient is 0.930, what...

Question 14

When r is not significantly different from 0, the best predictor of y is the ____________ of the data values of y.

Accepted Answer

The answer of When r is not significantly different from...

Question 15

Find the equation of the regression line.

Accepted Answer

The answer of Find the equation of the regression line....

Question 16

A correlation coefficient r was calculated to be 0.610. The coefficient of determination would be approximately __________.

Accepted Answer

The answer of A correlation coefficient r was calculated to...

Question 17

If the equation for the regression line is y' = -8x + 3, then the intercept of this line is
A) 6
B) 3
C) -5
D) -8

Accepted Answer

The intercept of the regression line is the value of y when x equals zero. 
So, setting x to 0 in the equation, we get:
y' = -8(0) + 3
y' = 3
Therefore, the intercept of the line is 3.

Question 18

What is the value of  when x = 3, if the equation of the regression line is  ?
A) 4.73
B) 5.29
C) 34.5
D) 11.7

Accepted Answer

The answer of What is the value of  when...

Question 19

Regression is a statistical method used to describe the nature of the relationship between variables.

Accepted Answer

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps in understanding how changes in the independent variable influence the dependent variable.

Question 20

A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
a. Draw a scatter plot.
b. Determine the regression line equation and plot the regression line
on the scatter plot.

Accepted Answer

The answer of A realtor wanted to determine if there...

Quiz 10: Correlation and Regression

The equation of a regression line is . What is the intercept of this line?

Using a regression line of , a value of x = 3.6 would result in a predicted value of .

A correlation coefficient r was calculated to be 0.830. The coefficient of nondetermination would be 0.170.

A regression line was calculated as . The slope of this line is -3.2.

If the correlation coefficient is 0.790, what is the explained variation?

If the equation for the regression line is y' = 7x - 9, then a value of x = 2 will result in a predicted value for y of

The formula for the coefficient of nondetermination is 1.00 - r2 .

If the equation for the regression line is y' = -4x + 3, then the slope of this line is

The variation due to chance, found by the formula __________, is called the unexplained variation.

A regression line can be used to show trends in data.

If the equation for the regression line is y' = 8x + 4, then a value of x = -3 will result in a predicted value for y of

If the correlation coefficient is 0.930, what is the unexplained variation?

When r is not significantly different from 0, the best predictor of y is the ____________ of the data values of y.

Find the equation of the regression line.

A correlation coefficient r was calculated to be 0.610. The coefficient of determination would be approximately __________.

If the equation for the regression line is y' = -8x + 3, then the intercept of this line is

What is the value of when x = 3, if the equation of the regression line is ?

Regression is a statistical method used to describe the nature of the relationship between variables.

A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home. a. Draw a scatter plot. b. Determine the regression line equation and plot the regression line on the scatter plot.

The formula for the coefficient of nondetermination is 1.00 - r² .