Question 1

Which of the following assertions is true about the regression line?
A) The regression line is also called the least cubes line and is found minimizing the sum of the cubes of the residuals.
B) It is found minimizing the sum of the residuals squared, but-even though it would be unnecessarily complicated-it could also be found minimizing the sum of the residuals cubed.
C) Depending on the data, some regression lines could have only positive residuals.
D) Depending on the data, some regression lines could have all residuals equal to zero.
E) Depending on the data, some regression lines could have only negative residuals.

Accepted Answer

The answer of Which of the following assertions is true...

Question 2

The following residuals plot indicates ___. 
A) a nonlinear relation
B) a nonconstant error variance
C) the simple regression assumptions are met
D) the sample is biased
E) a random sample

Accepted Answer

The answer of The following residuals plot indicates ___. 
A)...

Question 3

A simple regression model resulted in a sum of squares of error of 125 (i.e., SSE = 125), and the standard error is 3.95. This model is for ___ pairs of data.
A) 8
B) 9
C) 10
D) 11
E) 12

Accepted Answer

The formula for SSE is SSE = ∑(yi - ŷ)2, where yi is the observed value, and ŷ is the predicted value. The larger the SSE, the worse the model's fit to the data. The standard error is a measure of the variability of the residuals (i.e., the distance between the predicted values and the observed values). Higher standard errors indicate greater variability, which typically means a worse model fit.
The formula for standard error is SE = sqrt(SSE / (n - 2)), where n is the number of data points. Solving for n, we get n = (SSE / SE2) + 2. Substituting in the given values, we get n = (125 / 3.952) + 2, which evaluates to approximately 10. Therefore, the regression model is for 10 pairs of data.

Question 4

Suppose for a given data set the regression equation is: y = 54.78 + 1.45x, and the point (0.00, 24.78) is in the data set. The residual for this point is ___.
A) 24.78
B) −24.78
C) 0.00
D) 30.00
E) −30.00

Accepted Answer

The predicted value of y when x = 0.00 is 54.78. The actual y value is 24.78. The residual is the actual y minus the predicted y, which is 24.78 - 54.78 = -30.00.

Question 5

A simple regression model developed for 12 pairs of data resulted in a sum of squares of error, SSE = 246. The standard error of the estimate is ___.
A) 24.6
B) 4.96
C) 20.5
D) 4.53
E) 12.3

Accepted Answer

The formula for the standard error of the estimate is the square root of SSE divided by the degrees of freedom (n-2). With 12 pairs of data, the degrees of freedom is 12-2 = 10. So, the standard error of the estimate is sqrt(246/10) = 4.96. Choice B is the correct answer.

Question 6

A simple regression model developed for ten pairs of data resulted in a sum of squares of error, SSE = 125. The standard error of the estimate is ___.
A) 12.5
B) 3.5
C) 15.6
D) 3.95
E) 25

Accepted Answer

The formula for standard error of the estimate is:

SE = square root(SSE / (n-2))

where n is the number of pairs of data.

Substituting given values, we get:

SE = square root(125 / (10-2)) = 3.95

Therefore, the correct answer is D.

Question 7

The assumptions underlying simple regression analysis include ___.
A) the error terms are exponentially distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are independent

Accepted Answer

Simple regression analysis assumes that the error terms (residuals) are independent of each other, meaning that the value of one residual does not affect the value of another residual.

Question 8

The assumption of constant error variance in regression analysis is called ___.
A) heteroscedasticity
B) homoscedasticity
C) residuals
D) linearity
E) nonnormality

Accepted Answer

Constant error variance means that the variance of the errors/residuals is the same across all levels of the independent variables. This is called homoscedasticity. Heteroscedasticity, on the other hand, is when the variance of the errors is not constant across levels of the independent variables. Residuals are the differences between the predicted values and the actual values. Linearity refers to the relationship between the independent and dependent variables being linear. Nonnormality refers to the distribution of the errors not being normal.

Question 9

In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, S_xx= 89.333 and S_e= 3.44. A 95% confidence interval for the average of y when x = 8 is ___. A) (9.13, 17.05) B) (2.75, 23.43) C) (10.31, 15.86) D) (3.56, 22.62) E) (12.09, 14.09)

Accepted Answer

The answer of In the regression equation, y = 2.164...

Question 10

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The observed t value is ___. A) 3.752 B) 3.852 C) 3.972 D) 3.985 E) 3.995

Accepted Answer

The observed t value is calculated using the formula t = b / (Se / sqrt(Sxx)), where b is the slope. Substituting the given values, t = 1.3657 / (3.44 / sqrt(89.333)) = 3.752.

Question 11

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___. A) 2.776 B) 2.132 C) 2.015 D) 1.943 E) 1.782

Accepted Answer

The answer of A researcher has developed the regression equation...

Question 12

A standard deviation of the error of the regression model is called the ___.
A) coefficient of determination
B) sum of squares of error
C) standard error of the estimate
D) R-squared
E) coefficient of correlation

Accepted Answer

The standard deviation of the error of the regression model is called the standard error of the estimate. The coefficient of determination (A) is the proportion of the variance in the dependent variable that can be explained by the independent variable(s). The sum of squares of error (B) is the sum of the squared differences between the actual and predicted values of the dependent variable. R-squared (D) is another term for the coefficient of determination. The coefficient of correlation (E) is a measure of the strength and direction of the linear relationship between two variables.

Question 13

One of the assumptions made in simple regression is that ___.
A) the error terms are exponentially distributed
B) the error terms have unequal variances
C) the model is linear
D) the error terms are dependent
E) the model is nonlinear

Accepted Answer

Simple regression assumes that the relationship between the dependent and independent variables is linear.

Question 14

A simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., S_e = 3.95), and the sum of squares of error (SSE) is ___. A) 187.23 B) 171.63 C) 156.03 D) 140.42 E) 124.82

Accepted Answer

The answer of A simple regression model for 10 pair...

Question 15

The total of the squared residuals is called the ___.
A) coefficient of determination
B) sum of squares of error
C) standard error of the estimate
D) R-squared
E) coefficient of correlation

Accepted Answer

The sum of squares of error represents the total loss of information or the total unexplained variation in the dependent variable due to the independent variables. It is calculated as the sum of the squared differences between the observed and predicted values.

Question 16

A researcher has developed a regression model from 26 pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The degrees of freedom for the critical table t value is ___.
A) 23
B) 24
C) 26
D) 25
E) 27

Accepted Answer

The degrees of freedom for a two-tailed test with 26 pairs of data points is 25 (n-2).

Question 17

One of the assumptions made in simple regression is that ___.
A) the error terms are normally distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are all equal

Accepted Answer

The assumption that the error terms are normally distributed is a key assumption in simple regression, as it allows for the use of statistical inference techniques such as hypothesis testing and confidence intervals. The other answer choices are not assumptions made in simple regression, but rather potential issues that may arise in the data.

Question 18

A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The critical table t value is ___.
A) 2.650
B) 3.012
C) 3.055
D) 2.718
E) 2.168

Accepted Answer

Since the researcher is conducting a two-tailed test with a 0.01 level of significance, the critical t value can be found using a t-distribution table with 12 degrees of freedom (n-2). Looking up 0.005 in the table (since it is a two-tailed test), we get a critical t value of 3.055. Therefore, choice C is the correct answer.

Question 19

The following residuals plot indicates ___. 
A) a nonlinear relation
B) a nonconstant error variance
C) the simple regression assumptions are met
D) the sample is biased
E) the sample is random

Accepted Answer

The residuals plot shows a funnel shape, which indicates a nonconstant error variance. The spread of the residuals increases as the predicted values increase, suggesting that the error variance is larger for higher values of the predictor variable. This violates one of the simple linear regression assumptions of equal error variance, also known as homoscedasticity.

Question 20

A researcher has developed a regression model from fifteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two?tailed test and ɑ = 0.10. The critical table t value is ___.
A) 1.771
B) 1.350
C) 1.761
D) 2.145
E) 2.068

Accepted Answer

For a two-tailed test with ɑ = 0.10 and degrees of freedom (df) = n - 2 = 15 - 2 = 13, the critical t value is approximately 1.771.

Quiz 14: Linear Correlation and Simple Linear Regression Analysis

Which of the following assertions is true about the regression line?

The following residuals plot indicates ___.

A simple regression model resulted in a sum of squares of error of 125 (i.e., SSE = 125) , and the standard error is 3.95. This model is for ___ pairs of data.

Suppose for a given data set the regression equation is: y = 54.78 + 1.45x, and the point (0.00, 24.78) is in the data set. The residual for this point is ___.

A simple regression model developed for 12 pairs of data resulted in a sum of squares of error, SSE = 246. The standard error of the estimate is ___.

A simple regression model developed for ten pairs of data resulted in a sum of squares of error, SSE = 125. The standard error of the estimate is ___.

The assumptions underlying simple regression analysis include ___.

The assumption of constant error variance in regression analysis is called ___.

In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, S_xx= 89.333 and S_e= 3.44. A 95% confidence interval for the average of y when x = 8 is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The observed t value is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___.

A standard deviation of the error of the regression model is called the ___.

One of the assumptions made in simple regression is that ___.

A simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., S_e = 3.95) , and the sum of squares of error (SSE) is ___.

The total of the squared residuals is called the ___.

A researcher has developed a regression model from 26 pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The degrees of freedom for the critical table t value is ___.

One of the assumptions made in simple regression is that ___.

A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The critical table t value is ___.

The following residuals plot indicates ___.

A researcher has developed a regression model from fifteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two?tailed test and ɑ = 0.10. The critical table t value is ___.

Quiz 14: Linear Correlation and Simple Linear Regression Analysis

Which of the following assertions is true about the regression line?

The following residuals plot indicates ___.

A simple regression model resulted in a sum of squares of error of 125 (i.e., SSE = 125) , and the standard error is 3.95. This model is for ___ pairs of data.

Suppose for a given data set the regression equation is: y = 54.78 + 1.45x, and the point (0.00, 24.78) is in the data set. The residual for this point is ___.

A simple regression model developed for 12 pairs of data resulted in a sum of squares of error, SSE = 246. The standard error of the estimate is ___.

A simple regression model developed for ten pairs of data resulted in a sum of squares of error, SSE = 125. The standard error of the estimate is ___.

The assumptions underlying simple regression analysis include ___.

The assumption of constant error variance in regression analysis is called ___.

In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, Sxx= 89.333 and Se= 3.44. A 95% confidence interval for the average of y when x = 8 is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, Sxx = 89.333, and Se = 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The observed t value is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, Sxx = 89.333, and Se = 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___.

A standard deviation of the error of the regression model is called the ___.

One of the assumptions made in simple regression is that ___.

A simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., Se = 3.95) , and the sum of squares of error (SSE) is ___.

The total of the squared residuals is called the ___.

A researcher has developed a regression model from 26 pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The degrees of freedom for the critical table t value is ___.

One of the assumptions made in simple regression is that ___.

A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The critical table t value is ___.

The following residuals plot indicates ___.

A researcher has developed a regression model from fifteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two?tailed test and ɑ = 0.10. The critical table t value is ___.

In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, S_xx= 89.333 and S_e= 3.44. A 95% confidence interval for the average of y when x = 8 is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The observed t value is ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___.

A simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., S_e = 3.95) , and the sum of squares of error (SSE) is ___.