QMB Chapter 14

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. What is the value of sb1 ?

.09038

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term ɛ is a random variable with a mean or expected value of:

0

In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is:

0.6

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. Predict approximately how many people will use the public pool in a day when the temperature is 90 degrees.

131

Which of the following statements is false?

Regression analysis can be interpreted as a procedure for establishing a cause-and-effect relationship between variables.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Identify the independent and dependent variables.

The independent variable is the advertising expenses, and the dependent variable is sales.

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. Test for a significant relationship between the number of people who use the public pool and the outside temperature. Use ⍺ =.05. State your conclusion.

The p-value < .05. The data provide evidence of a significant relationship between the number of people who use the public pool and the outside temperature.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Create a scatter diagram in order to answer the following question: What does the scatter diagram indicate about the relationship between the two variables?

The scatter diagram indicates a positive relationship between advertising expenses and sales.

If the coefficient of determination is a positive value, then the coefficient of correlation:

can be either negative or positive.

The value of the coefficient of correlation (r):

can be equal to the value of the coefficient of determination (r2).

The coefficient of determination:

cannot be negative.

Observations with extreme values for the independent variables are called:

high leverage points.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term follows ɛ a(n) _____ distribution for all values of x.

normal

A graph of the standardized residuals plotted against values of the normal scores that helps to determine whether the assumption that the error term has a normal probability distribution appears to be valid is called a:

normal probability plot.

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n):

residual.

An F test, based on the F probability distribution, can be used to test for:

significance in regression.

The following data show the results of an aptitude test and the grade point average of 10 students. Does the t test indicate a significant relationship between GPA and Aptitude Test Score? State the test statistic, and then state your conclusion using ⍺ = .05.

t = 6.25. The p- value is less than .05, so the evidence is sufficient to conclude that a significant relationship exists between GPA and Aptitude Test Scores.

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. State the test statistic and p-value used to determine whether the number of people who use the public pool is related to the outside temperature.

t = 8.98 and p-value = .000

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, what distribution do confidence and prediction intervals follow?

t distribution

If a residual plot of x versus the residuals, y - ŷ, shows a non-linear pattern, then we should conclude that:

the regression model is not an adequate representation of the relationship between the variables.

The tests of significance in regression analysis are based on assumptions about the error term ɛ . One such assumption is that the variance of ɛ, denoted by 𝝈2, is:

the same for all values of x.

In a regression analysis, an outlier will always increase:

the value of the correlation.

The following data show the results of an aptitude test and the grade point average of 10 students. The t test for a significant relationship between GPA and Aptitude Test Score is based on a tdistribution with _____ degrees of freedom.

8

The estimated regression equation, , can be used to predict a company's sales volume (y), in millions, based upon its advertising expenditure (x), in $10,000s. What is the company's predicted sales volume if they spend $500,000 on advertising?

Approximately $29 million

The following data show the results of an aptitude test and the grade point average of 10 students. If GPA and Aptitude Test Scores are linearly related, which of the following must be true?

B1 /= 0

The following data show the results of an aptitude test and the grade point average of 10 students. At 95% confidence, test to determine if the model is significant (Perform an F test). What is the test statistic and p-value ?

F = 39.07 and p-value = .0002

Influential observations always:

None of the above are correct.

When studying the relationship between two quantitative variables, an interval estimate of the mean value of y for a given value of x is called a(n):

a.confidence interval.

When working with regression analysis, an outlier is:

any observation that does not fit the trend shown by the remaining data.

Suppose a residual plot of x verses the residuals, y - ŷ, shows a nonconstant variance. In particular, as the values of x increase, suppose that the values of the residuals also increase. This means that:

as the values of x get larger, the ability to predict y becomes less accurate.

If a significant relationship exists between x and y and the coefficient of determination shows that the fit is good, the estimated regression equation should be useful for:

estimation and prediction.

Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid is called a:

residual plot.

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

dependent variable.

The model developed from sample data that has the form y(hat) = bo +b1x is known as the:

estimated regression equation.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the values of ɛ are:

independent

An observation that has a strong influence or effect on the regression results is called a(n):

influential observation.

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

least squares line.

The tests of significance in regression analysis are based on several assumptions about the error term ɛ. Additionally, we make an assumption about the form of the relationship between x and y. We assume that the relationship between x and y is:

linear

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, the appropriate degrees of freedom are:

n - 2.

When studying the relationship between two quantitative variables, whenever we want to predict an individual value of y for a new observation corresponding to a given value of x, we should use a(n):

prediction interval.

The mathematical equation E(y) = Bo + B1x relating the independent variable to the expected value of the dependent variable, , is known as the:

regression equation.

In regression analysis, the equation in the form y = 𝛽0 + 𝛽1x + ε is called the:

regression model.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Use the least squares method to develop the estimated regression equation.

y(hat) = - 10.42 + 0.79x

Following is a portion of the computer output for a regression analysis relating y = number of people who use the public pool to x = the outside temperature. What is the estimated regression equation?

y(hat) = 57.912 +0.81138x

In a regression analysis, the error term ε is a random variable with a mean or expected value of

zero