QMB 3200 Module 7 Chapter 15

The following regression model has been proposed to predict sales at a gas station: y=10-4x1+7x2+18x3 , where x 1= competitor's previous day's sales (in $1,000s), x 2= population within 5 miles (in 1,000s), x 3= 1 if any form of advertising was used, 0 if otherwise, and y = sales (in $1,000s). Predict sales (in dollars) for a store with competitor's previous day's sale of $5,000, a population of 15,000 within 5 miles, and five radio advertisements.

$113,000 -- y=10-4(5)+7(15)+18(1) = 113,000

The following estimated regression model was developed to predict yearly income (in $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female) for a sample of 50 engineers. y=-10+4x1+7x2 What is the estimated income of a 30 year old female?

$117,000 -- y=-10+4(30)+7(1) = 117,000

The following regression model has been proposed to predict sales at a gas station: y=10-4x1+7x2+18x3 , where x1= competitor's previous day's sales (in $1,000s), x2= population within five miles (in 1,000s), x3= 1 if any form of advertising was used, 0 if otherwise, and y = sales (in $1,000s). Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within five miles, and six radio advertisements.

$86,000 -- y=10-4(3)+7(10)+18(1) = $86000

In a multiple regression analysis, if the estimated regression equation is y=.7904+.2345x1-.7892x2, find the estimated value, given the first and second independent variables as 10 and 20, respectively

-12.6486 -- y=.7904+.2345(10)-.7892(20) = -12.6486

In a multiple regression analysis, any observation with a standardized residual less than ____ or greater than ____ is known as an outlier

-2;2

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is:

.75 -- R^2 = SSR/SST = 600/200+600 = 600/800 = .75

In the multiple regression model, the error term E is assumed to have a mean of:

0

Suppose after calculating an estimated multiple regression equation, we find that the value of R^2 is .9201. Interpret this value

92.01% the variability in y can be explained by the estimated regression equation

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares: SSE= 306, SST= 1800. At α=.05, test to determine whether or not the model is significant. State the F value and your conclusion

F=36.62; p-value < .05. The model is significant -- complete Anova table

Suppose a multiple coefficient of determination coming from a regression analysis with 50 observations and 3 independent variables is .8455. Calculate the adjusted multiple coefficient of determination.

R-Sq(adj) = 83.54% -- 1-(1-.8455)(50-1/50-3-1) = 1-(.1545)(49/46) = .8354

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y)=B0+B1x1+B2x2+........+Bpxp is called:

a multiple regression equation

The mathematical equation that explains how the dependent variable y is related to several independent variables and has the form y=B0+B1x1+....+Bpxp+E is called

a multiple regression model

The multiple regression equation based on the sample data, which has the form of y=b0+b1x1+b2x2+......+bpxp is called

an estimated multiple regression equation

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(n):

confidence interval

A variable used to model the effect of categorical independent variables is called a(n):

dummy variable

The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the:

error term, E

A regression was performed on a sample of 16 observations. The estimated equation is y=3.5-15.54x1+1.4x2+12.6x3. The standard errors for the coefficients are sb1=4.2, sb2=5.6, and sb3=2.8. Test for the significance of β1, β2, and β3 at the 5% level of significance.

factor x1 and factor x3 are statistically significant -- 15.54/4.2=-3.7 (less than .05 so significant)

Which of the following variables is categorical?

gender

A multiple regression model has the form y=5+6x1-7x2. As x1 increases by 1 unit (holding x2 constant), the dependent variable is expected to:

increase by 6 units

A regression model between sales ( y in $1,000) and unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function: y=5-3x1+4x2 . The coefficient of the unit price indicates that if the unit price is:

increased by $1 (holding advertisement constant), the sales are expected to decrease by $3000

In general R^2 always ______ as independent variables are added to the regression model

increases

In a multiple regression model, the values of the error term, E, are assumed to be:

independent of each other

When we conduct significance tests for a multiple regression relationship, the t test can be conducted for each of the independent variables in the model. Each of those tests are called tests for:

individual significance

If a categorical variable has k levels, then:

k-1 dummy variables are needed

The method to develop the estimated regression equation that minimizes the sum of squared residuals is called the:

least squares method

The term used to describe the case when the independent variables in a multiple regression model are correlated is:

multicollinearity

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is called the:

multiple coefficient of determination

The study of how a dependent variable y is related to two or more independent variables is called:

multiple regression analysis

In a multiple regression model, the values of the error term, E, are assumed to be:

normally distributed

When we conduct significance tests for a multiple regression relationship, the F test will be used as the test for:

overall significance

All things held constant, which interval will be wider: a confidence interval or a prediction interval?

prediction interval

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(n):

prediction interval

Since the multiple regression equation generates a plan or surface, the graph is called a:

response surface

In a multiple regression model, the variance of the error term, E, is assumed to be:

the same for all values of x1,x2.....xp

In a multiple regression analysis:

there can be several independent variables, but only one dependent variable

Dummy variables must always have:

values of either 0 or 1

A multiple regression model has the form y=5+6x1-7x2. predict y when and x1=2 and x2=-2

y=31 -- y=5+6(2)-7(-2) = 5+12+14 = 31