E2 - Chapter 7 Linear Regression - BADM

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$86,000

What would be the coefficient of determination if the total sum of squares (SST) is 30 and the sum of squares due to regression (SSR) is 27?

0.90

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 22.21 and the sum of squares due to error (SSE) is 6.89?

15.32

When there are many independent variables to consider, special procedures are sometimes employed to select the independent variables to include in the regression model. All of the following are examples of variable selection procedures except for

overfitting.

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slope

When we use the estimated regression equation to develop an interval that can be used to predict the mean for ALL units that meet a particular set of given criteria, that interval is called a

confidence interval.

A variable used to model the effect of categorical independent variables is called a

dummy variable.

In the simple linear regression model, the ________ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between x and y.

error term

The _____ is the range of values of the independent variables in the data used to estimate the regression model.

experimental region

Simple linear regression refers to the type of regression analysis for which the relationship between the independent variable and dependent variable are approximated by a(n)

exponential curve.

Prediction of the value of the dependent variable outside the experimental region is called

extrapolation.

The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as

hypothesis testing.

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

normal

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as

statistical inference.

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

Found below is Excel output from a quadratic regression analysis based upon the number of cars each employee sold during the most recent sales period and the number of months each salesperson has been employed by the company. https://i.gyazo.com/ce23e530d009a82ced32d8aaea096a5f.png Based upon the p-values for "Month" and "Month Squared", what can we conclude about the current model?

Because both p-values are substantially less than 0.05, we can conclude that adding Months Squared to the model involving Months is significant.

Found below is Excel output from a quadratic regression analysis based upon the number of cars each employee sold during the most recent sales period and the number of months each salesperson has been employed by the company. https://i.gyazo.com/464fd25b41e86a8b0a384e3a00e94801.png Which of the following gives the correct quadratic regression model?

Sales = 21.92 - 24.55(Months Employed) + 8.06(Months Employed)2

Found below is Excel output from a quadratic regression analysis based upon the number of cars each employee sold during the most recent sales period and the number of months each salesperson has been employed by the company. https://i.gyazo.com/9e353c5d415b3f374ad405acb074f13c.png Interpret the coefficient of determination for this regression model.

This regression model explains approximately 95.5% of the variation in cars sold for our sample data.

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a multiple regression model.

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

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

Two variables have a positive linear correlation. As the dependent variable increases, the independent variable will

increase

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

independent.

When we use the estimated regression equation to develop an interval that can be used to predict the mean for a specific unit that meets a particular set of given criteria, that interval is called a

prediction interval.

What type of regression model should be used when there is a nonlinear relationship between the independent and dependent variables which is fit by including the independent variable and the square of the independent variable?

quadratic regression model

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the

residual.

When determining the best estimated regression equation to model a set of data, the procedure that uses an iterative variable selection procedure that considers adding an independent variable and removing an independent variable at each step is called

stepwise selection.

The _____ is a measure of the error that results from using the estimated regression equation to predict the values of the dependent variable in a sample.

sum of squares due to error (SSE)

The following data show the results of an aptitude test and the grade point average of 10 students. https://i.gyazo.com/c245d03a425926d21f39dd79f2d6ca81.png Does the t test indicate a significant relationship between GPA and Aptitude Test Score? State the test statistic, and then state your conclusion. Use ∝ = 0.05.

t = 6.25. The p-value is less than 0.05, so there is evidence is sufficient to conclude that a significant relationship exists between GPA and Aptitude Test Scores.

The tests of significance in regression analysis are based on assumptions about the error term ε. One such assumption is that the variance of ε, denoted by σ 2 , is

the same for all values of x.

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y-intercept

Consider the Excel output for a simple linear regression model. What is the regression model? https://i.gyazo.com/0b7ddd2f7a15c3fe039aab9c9d8cb509.png

y^ = 2.64 + 0.016x

When the mean value of the response variable is independent of variation in the predictor variable, the slope of the regression line is

zero.

The following data show the results of an aptitude test and the grade point average of 10 students. https://i.gyazo.com/f8889b915b2c776132e23113f2f11759.png If GPA and Aptitude Test Scores are linearly related, which of the following must be true?

β ≠ 0