Question 1

In a regression analysis, the regression equation is given by y = 12 - 6x.If SSE = 510 and SST = 1000, then the coefficient of correlation is
A) -.7.
B) +.7.
C) .49.
D) -.49.

Accepted Answer

The coefficient of determination (R^2) is calculated as 1 - (SSE/SST) = 1 - (510/1000) = 0.49. The coefficient of correlation (R) is the square root of R^2, which gives ±0.7. Given the negative slope (-6) in the regression equation, the correlation is negative, hence -.7.

Question 2

In simple linear regression analysis, which of the following is not true? A) The F test and the t test yield the same conclusion. B) The F test and the t test may or may not yield the same conclusion. C) The relationship between x and y is represented by a straight line. D) The value of F = t².

Accepted Answer

The answer of In simple linear regression analysis, which of...

Question 3

Larger values of r² imply that the observations are more closely grouped about the A) average value of the independent variables. B) average value of the dependent variable. C) least squares line. D) origin.

Accepted Answer

r² is the correlation coefficient between the observed values of the dependent variable and the predicted values from the least squares line. Larger values of r² indicate a stronger linear relationship between the independent and dependent variables, and that the observations are more closely grouped about the least squares line. Therefore, the best choice is C, the least squares line.

Question 4

In a regression analysis, the coefficient of determination is .4225.The coefficient of correlation in this situation is A) -.65 if b₁ is negative. B) .1785. C) .18 if b₁ is positive. D) .4225.

Accepted Answer

The answer of In a regression analysis, the coefficient of...

Question 5

In regression analysis, if the independent variable is measured in pounds, the dependent variable
A) must also be in pounds.
B) must be in some unit of weight.
C) cannot be in pounds.
D) can be measured in any units.

Accepted Answer

The units of the dependent variable in a regression analysis are independent of the units of the independent variable. The dependent variable can be measured in any units, regardless of the units of the independent variable.

Question 6

If the coefficient of determination is equal to 1, then the coefficient of correlation
A) must also be +1.
B) can be either -1 or +1.
C) can be any value between -1 to +1.
D) must be -1.

Accepted Answer

The coefficient of determination (R^2) being equal to 1 indicates a perfect linear relationship between two variables. The coefficient of correlation (r) describes the direction of this relationship, which can be perfectly positive (+1) or perfectly negative (-1), hence why it can be either -1 or +1 when R^2 is 1.

Question 7

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
A) .85%.
B) 85%.
C) .7225%.
D) 72.25%.

Accepted Answer

The coefficient of determination (r-squared) is the square of the coefficient of correlation (r), which represents the percentage of variation in the dependent variable explained by the variation in the independent variable. Therefore, if the coefficient of correlation is .8, the coefficient of determination is .8^2 = .64, which means that 64% of the variation in the dependent variable is explained by the variation in the independent variable. To convert this to a percentage, we multiply by 100, so the answer is 64 x 1.5625 = 62.25%. The closest answer choice is D, which is 72.25%, but that is not the correct answer.

Question 8

In a regression analysis, if SSE = 200 and SSR = 400, then the coefficient of determination is
A) .67.
B) .50.
C) .40.
D) .20.

Accepted Answer

The coefficient of determination, $R^2$, is calculated as $SSR / (SSR + SSE)$. Plugging in the given values, $R^2 = 400 / (400 + 200) = 400 / 600 = 2 / 3 = .67$.

Question 9

?Which of the following is correct?
A) ?SSE =SSR + SST
B) ?SSR = SSE + SST
C) ?SST = SSR +SSE
D) ?SST = SSR - SSE

Accepted Answer

The formula for total sum of squares (SST) is:
SST = SSR + SSE
Where, SSR = sum of squares of regression and SSE = sum of squares of error.
Thus, the correct expression is:
SST = SSR + SSE
Therefore, option C is the correct answer.

Question 10

If there is a very weak correlation between two variables, then the coefficient of determination must be
A) much larger than 1, if the correlation is positive.
B) much smaller than -1, if the correlation is negative.
C) equal to one.
D) closer or equal to zero.

Accepted Answer

The coefficient of determination, also known as R-squared, is a measure of how much of the variation in one variable is explained by the variation in the other variable. If there is a very weak correlation between two variables, it means that there is not much variation in one variable that can be explained by the variation in the other variable, and vice versa. Therefore, the coefficient of determination will be close to or equal to zero, indicating a low level of explanation or predictability.

Question 11

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
A) the correlation model.
B) the regression model.
C) correlation analysis.
D) estimation analysis.

Accepted Answer

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called the regression model. The other options are incorrect because correlation analysis does not provide an equation, it only measures the strength of the relationship between variables, and estimation analysis is not specific enough to describe the relationship between two variables.

Question 12

In regression and correlation analysis, if SSE and SST are known, then with this information the
A) coefficient of determination can be computed.
B) slope of the regression line can be computed.
C) y-intercept can be computed.
D) x-intercept can be computed.

Accepted Answer

The coefficient of determination (r-squared) is calculated as SSE/SST, where SSE is the sum of squares of residuals and SST is the total sum of squares. Therefore, if SSE and SST are known, the coefficient of determination can be computed. The slope of the regression line and y-intercept can be calculated using other information such as the mean and standard deviation of the variables, and the x-intercept may not exist at all.

Question 13

In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then
A) there is a positive correlation between x and y.
B) if x is increased, y must also increase.
C) if y is increased, x must also increase.
D) the estimated regression line intercepts the positive y-axis.

Accepted Answer

The y-intercept represents the value of y when x is equal to zero, so if the y-intercept is positive, it means that the estimated regression line crosses the positive y-axis. This does not imply any correlation between x and y or a cause-and-effect relationship between them. Additionally, it does not necessarily mean that y will increase if x increases or vice versa.

Question 14

In a regression and correlation analysis, if r² = 1, then A) SSE must also be equal to one. B) SSE must be equal to zero. C) SSE can be any positive value. D) SSE must be negative.

Accepted Answer

The correlation coefficient (r) measures the strength and direction of the relationship between two variables. A perfect positive correlation between two variables is denoted by r = 1. In this case, r² = 1 indicates a perfect positive linear relationship between the variables ^{2 and}. In a regression analysis, the sum of squared errors (SSE) measures the variability that is not explained by the regression equation. If r = 1, then the regression equation perfectly explains the relationship between the variables, and there is no variability left unexplained. This means that SSE must be equal to zero, as all the data points fall on the regression line. Therefore, the best choice is B: SSE must be equal to zero.

Question 15

In a regression analysis, the coefficient of correlation is .15.The coefficient of determination in this situation is
A) .3873.
B) .0225.
C) 4.00.
D) 2.56.

Accepted Answer

The coefficient of determination is the square of the coefficient of correlation. Therefore, in this situation, the coefficient of determination is 0.15^2 = 0.0225, which is option B.

Question 16

In a regression and correlation analysis, if r² = 1, then A) SSE = SST. B) SSE = 1. C) SSR = SSE. D) SSR = SST.

Accepted Answer

When $r = 1$, it indicates a perfect positive linear relationship between the variables. This means all the points lie exactly on the regression line, and there is no variation of the actual values from the predicted values. Therefore, the Sum of Squares for Regression (SSR), which measures how well the regression line fits the data, is equal to the Total Sum of Squares (SST), which measures the total variation in the data. This implies that there is no error (SSE, Sum of Squares for Error) because all variation is perfectly explained by the regression line.

Question 17

Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. ​  = 120 - 10x
​
Based on the above estimated regression equation, if price is increased by 3units, then demand is expected to
A) increase by 120 units.
B) decrease by 100 units.
C) increase by 30 units.
D) decease by 30 units.

Accepted Answer

According to the estimated regression equation, for every unit increase in price, the demand is expected to decrease by 10 units. Therefore, if the price is increased by 3 units, the demand is expected to decrease by 3 x 10 = 30 units.

Question 18

Correlation analysis is used to determine
A) the equation of the regression line.
B) the strength of the linear relationship between the dependent and the independent variables.
C) a specific value of the dependent variable for a given value of the independent variable.
D) a cause-and-effect relationship between the dependent and the independent variables.

Accepted Answer

Correlation analysis is used to determine the strength and direction of the linear relationship between two variables. It does not establish causation or provide an equation for prediction, so options A, C, and D are incorrect.

Question 19

In regression analysis, the independent variable is
A) used to predict other independent variables.
B) used to predict the dependent variable.
C) the variable that is not used for prediction.
D) the variable that is being predicted.

Accepted Answer

The independent variable in regression analysis is the variable that is used to predict the dependent variable.

Question 20

In regression analysis, the variable that is being predicted is the
A) dependent variable.
B) independent variable.
C) intercept variable.
D) error variable.

Accepted Answer

In regression analysis, the variable that is being predicted is the dependent variable. The independent variable is used to predict the dependent variable. The intercept variable represents the value of the dependent variable when all independent variables are equal to zero. The error variable represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

Quiz 14: Simple Linear Regression

In a regression analysis, the regression equation is given by y = 12 - 6x.If SSE = 510 and SST = 1000, then the coefficient of correlation is

In simple linear regression analysis, which of the following is not true?

Larger values of r² imply that the observations are more closely grouped about the

In a regression analysis, the coefficient of determination is .4225.The coefficient of correlation in this situation is

In regression analysis, if the independent variable is measured in pounds, the dependent variable

If the coefficient of determination is equal to 1, then the coefficient of correlation

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

In a regression analysis, if SSE = 200 and SSR = 400, then the coefficient of determination is

?Which of the following is correct?

If there is a very weak correlation between two variables, then the coefficient of determination must be

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

In regression and correlation analysis, if SSE and SST are known, then with this information the

In a simple linear regression analysis (where y is a dependent and x an independent variable) , if the y-intercept is positive, then

In a regression and correlation analysis, if r² = 1, then

In a regression analysis, the coefficient of correlation is .15.The coefficient of determination in this situation is

In a regression and correlation analysis, if r² = 1, then

Regression analysis was applied between demand for a product (y) and the price of the product (x) , and the following estimated regression equation was obtained. = 120 - 10x Based on the above estimated regression equation, if price is increased by 3units, then demand is expected to

Correlation analysis is used to determine

In regression analysis, the independent variable is

In regression analysis, the variable that is being predicted is the

Quiz 14: Simple Linear Regression

In a regression analysis, the regression equation is given by y = 12 - 6x.If SSE = 510 and SST = 1000, then the coefficient of correlation is

In simple linear regression analysis, which of the following is not true?

Larger values of r2 imply that the observations are more closely grouped about the

In a regression analysis, the coefficient of determination is .4225.The coefficient of correlation in this situation is

In regression analysis, if the independent variable is measured in pounds, the dependent variable

If the coefficient of determination is equal to 1, then the coefficient of correlation

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

In a regression analysis, if SSE = 200 and SSR = 400, then the coefficient of determination is

?Which of the following is correct?

If there is a very weak correlation between two variables, then the coefficient of determination must be

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

In regression and correlation analysis, if SSE and SST are known, then with this information the

In a simple linear regression analysis (where y is a dependent and x an independent variable) , if the y-intercept is positive, then

In a regression and correlation analysis, if r2 = 1, then

In a regression analysis, the coefficient of correlation is .15.The coefficient of determination in this situation is

In a regression and correlation analysis, if r2 = 1, then

Regression analysis was applied between demand for a product (y) and the price of the product (x) , and the following estimated regression equation was obtained. ​ = 120 - 10x ​ Based on the above estimated regression equation, if price is increased by 3units, then demand is expected to

Correlation analysis is used to determine

In regression analysis, the independent variable is

In regression analysis, the variable that is being predicted is the

Larger values of r² imply that the observations are more closely grouped about the

In a regression and correlation analysis, if r² = 1, then

In a regression and correlation analysis, if r² = 1, then

Regression analysis was applied between demand for a product (y) and the price of the product (x) , and the following estimated regression equation was obtained. = 120 - 10x Based on the above estimated regression equation, if price is increased by 3units, then demand is expected to