Question 1

Explain what is meant by the term least squares regression model.

Accepted Answer

The answer of Explain what is meant by the term...

Question 2

A random sample of two variables, x and y, produced the following observations:  Compute the correlation coefficient for these sample data.
A) -0.9707
B) -0.2141
C) 0.5133
D) 0.8612

Accepted Answer

The answer of A random sample of two variables, x...

Question 3

A random sample of two variables, x and y, produced the following observations:  Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test.
A) Because t = -4.152 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.
B) Because t = -4.152 < -1.9432, do not reject the null hypothesis. Because the null hypothesis is not rejected, the sample data support the hypothesis that there is a negative linear relationship between x and y.
C) Because t = -9.895 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.
D) Because t = -9.895 < -1.9432, do not reject the null hypothesis. Because the null hypothesis is not rejected, the sample data support the hypothesis that there is a negative linear relationship between x and y.

Accepted Answer

The answer of A random sample of two variables, x...

Question 4

Which of the following statements is true?
A) The interval estimate for predicting a particular value of y given a specific x will be narrower than the interval estimate for the average value of y given a particular x.
B) The higher the r-square value, the wider will be the prediction interval based on a simple linear regression model.
C) The prediction interval generated from a simple linear regression model will be narrowest when the value of x used to generate the predicted y value is close to the mean value of x.
D) The prediction interval generated from a simple linear regression model will be widest when the value of x used to generate the predicted y value is close to the mean value of x.

Accepted Answer

The prediction interval for a single prediction in regression analysis tends to be narrowest when the value of x is close to the mean of x. This is because the further away from the mean of x, the greater the uncertainty in the prediction, leading to wider intervals.

Question 5

If you were going to develop a scatter plot for the purpose of determining whether one of the assumptions of the regression model is being satisfied, which of the following is true?
A) The plot should illustrate a bell-shaped distribution to show that the residuals are normally distributed.
B) The horizontal axis should show the fitted values for the dependent variable.
C) The plot should illustrate a cone shaped look.
D) The points should fall in a straight line.

Accepted Answer

The scatter plot for checking assumptions in a regression model typically plots the residuals on the vertical axis against the fitted values on the horizontal axis. This helps in assessing the homoscedasticity of residuals, which is a key assumption in regression analysis.

Question 6

What factors are of importance to an analyst when linear regression analysis is used for descriptive purposes?

Accepted Answer

The answer of What factors are of importance to an...

Question 7

The Public Utility Commission in a southern state is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in the following regression results:  Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet.

Accepted Answer

The answer of The Public Utility Commission in a southern...

Question 8

Explain what the correlation coefficient measures and some detail of the key issues associated with it. Be sure to also discuss the concept of spurious correlation.

Accepted Answer

The answer of Explain what the correlation coefficient measures and...

Question 9

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x. Also assume that n = 201 and that the standard error of the estimate is sε = 4.5. Find the approximate 95 percent prediction interval.
A) About 101 ----- 119
B) About 109.4 ----- 110.6
C) About 105.5 ----- 104.5
D) About 98.4 ----- 121.6

Accepted Answer

The approximate 95 percent prediction interval is given by:prediction ± 1.96 * sεwhere prediction is the predicted value, sε is the standard error of the estimate, and 1.96 is the z-score corresponding to a 95% confidence level.In this case, prediction = 110, sε = 4.5, so the approximate 95 percent prediction interval is:110 ± 1.96 * 4.5 = 110 ± 8.82 = (101.18, 118.82)Therefore, the correct answer is A: About 101 ----- 119.

Question 10

If a residual plot exhibits a curved pattern in the residuals, this means that:
A) the errors are not normally distributed.
B) there must be a curvilinear relation between x and y.
C) there is no significant relation between x and y.
D) there is a problem with constant variance.

Accepted Answer

A curved pattern in the residuals of a plot suggests that the relationship between the independent variable (x) and the dependent variable (y) is not linear, indicating a curvilinear relationship. This means that a linear model may not be the best fit for the data.

Question 11

Which of the following statements is true?
A) When using a simple linear regression analysis model for prediction purposes, the potential error in the forecast will be less when the value of x used to forecast y is closer to .
B) The accuracy of the regression forecast is improved if the standard error for the regression slope coefficient is reduced.
C) The use of regression analysis as a means of predicting the value for a dependent variable is not impacted by sampling error since the regression model uses all sample data to arrive at the regression
Model.
D) None of the above

Accepted Answer

The answer of Which of the following statements is true?
A)...

Question 12

Residual analysis is conducted to check whether regression assumptions are met. Which of the following is not an assumption made in simple linear regression?
A) Errors are independent of each other.
B) Errors are normally distributed.
C) Errors are linearly related to x.
D) Errors have constant variance.

Accepted Answer

The assumption in simple linear regression is that the relationship between the independent variable (x) and the dependent variable is linear, not that the errors themselves are linearly related to x. Errors are expected to be independent, normally distributed, and have constant variance.

Question 13

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected. These data are shown as follows:  Based upon these data, what is the approximate predicted value for tips if the total bill is $100?
A) $15.55
B) $20.61
C) $26.03
D) $12.88

Accepted Answer

The answer of A study was recently performed by the...

Question 14

In analyzing the residuals to determine whether the simple regression analysis satisfies the regression assumptions, which of the following is true?
A) The histogram of the residuals should be approximately bell-shaped.
B) The scatter plot of the residuals against the dependent variable should illustrate that the variation in residuals is the same over all levels of .
C) Neither A nor B are true.
D) Both A and B are true.

Accepted Answer

The histogram of the residuals should be approximately bell-shaped to satisfy the assumption of normality, and the scatter plot of the residuals against the dependent variable should show constant variance (homoscedasticity) across all levels of the independent variable, indicating both A and B are true.

Question 15

Which of the following is a correct interpretation for the regression slope coefficient?
A) For a one-unit change in y, we can expect the value of the independent variable to change by b1 units on average.
B) For each unit change in x, the dependent variable will change by b1 units.
C) The average change in y of a one-unit change in x will be b1 units.
D) The average change in x of a one-unit change in y will be b1 units.

Accepted Answer

The average change in y of a one-unit change in x will be b1 units.

Question 16

Explain why it is important to construct scatter plots prior to conducting regression analysis.

Accepted Answer

The answer of Explain why it is important to construct...

Question 17

An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study included 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use an alpha = 0.05
A) Because t = 2.50 > 1.7709, do not reject the null hypothesis. There is not sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this
Industry.
B) Because t = 2.50 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.
C) Because t = 3.13 > 1.7709, do not reject the null hypothesis. There is not sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this
Industry.
D) Because t = 3.13 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

Accepted Answer

The t-value calculated from the sample correlation (0.57) and sample size (15) indicates a significant positive correlation since it exceeds the critical t-value at alpha = 0.05, leading to the rejection of the null hypothesis.

Question 18

The following data for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling:  Compute the correlation coefficient.
A) 0.52
B) 0.71
C) 0.62
D) 0.89

Accepted Answer

The answer of The following data for the dependent variable,...

Question 19

A national job placement company is interested in developing a model that might be used to explain the variation in starting salaries for college graduates based on the college GPA. The following data were collected through a random sample of the clients with which this company has been associated.  Based on this sample information, determine the least squares regression model, determine what percent of the variation in starting salaries is explained by GPA, and test to determine whether the regression model is statistically significant at the 0.05 level of significance. Also, develop a scatter plot of the data and locate the regression line on the scatter plot.

Accepted Answer

The answer of A national job placement company is interested...

Quiz 14: Introduction to Linear Regression and Correlation Analysis

Explain what is meant by the term least squares regression model.

A random sample of two variables, x and y, produced the following observations: Compute the correlation coefficient for these sample data.

A random sample of two variables, x and y, produced the following observations: Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test.

Which of the following statements is true?

If you were going to develop a scatter plot for the purpose of determining whether one of the assumptions of the regression model is being satisfied, which of the following is true?

What factors are of importance to an analyst when linear regression analysis is used for descriptive purposes?

Explain what the correlation coefficient measures and some detail of the key issues associated with it. Be sure to also discuss the concept of spurious correlation.

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x. Also assume that n = 201 and that the standard error of the estimate is sε = 4.5. Find the approximate 95 percent prediction interval.

If a residual plot exhibits a curved pattern in the residuals, this means that:

Which of the following statements is true?

Residual analysis is conducted to check whether regression assumptions are met. Which of the following is not an assumption made in simple linear regression?

In analyzing the residuals to determine whether the simple regression analysis satisfies the regression assumptions, which of the following is true?

Which of the following is a correct interpretation for the regression slope coefficient?

Explain why it is important to construct scatter plots prior to conducting regression analysis.

The following data for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling: Compute the correlation coefficient.