qmb 3200 exam 3 ch15

The following regression model has been proposed to predict sales at a gas station: yhat = 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 yhat = 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 yhat = 10 - 4x1 + 7x2 + 18x3 x1 = competitors days sales (in $1,000s) = 5 x2 = population within 5 miles (in $1,000s) = 15 x3 = 1 if any form of advertising was used (it was) = 1 yhat = 10 - 4(5) + 7(15) + 18(1) y hat = $113,000

The following estimated regression model was developed to predict yearly income (yhat 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. yhat = -10 + 4x1 + 7x2 What is the estimated income of a 30-year-old female?

$117,000 yhat = -10 + 4x1 + 7x2 yhat = -10 + 4(30) + 7(1) yhat = $117,000

The following regression model has been proposed to predict sales at a gas station: yhat = 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 yhat = 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.

$86000 yhat = 10 - 4(3) + 7(10) + 18(1) = 86

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

-12.6486 yhat = .7904 + .2345x1 - .7892x2 yhat = .7904 + .2345(10) - .7892(20) yhat = -12.6486

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

-2;2

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

0

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

0.75 R^2 = SSR/SST SST = SSR + SSE R^2 = 600 / 200 + 600 R^2 = 600 / 800 = 0.75

From the given residual plot, identify the outlier(s), if any.

4.3, -2.6, and -2.5 Must look at visual table to find these. Any observation with a standardized residual of less than -2 or greater than +2 is known as an outlier.

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. F = MSR/MSE SST = SSR + SSE 1800 = SSR + 306 SSR = 1494 MSR = SSR/p 1494/8 = 186.75 MSE = SSE/n-p-1 = 306/69-8-1 = 5.1 F = MSR/MSE 186.75/5.1 = 36.62 Find p val, go to f table df num = p = 8 df den = n-p-1 = 60 at 0.05, critical val is 2.1 Determine significance F test stat (36.62) > F critical val (2.1) Significant

A regression was performed on a sample of 16 observations. The estimated equation is yhat = 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. t = b1/sb1 t = -15.54/4.2 = -3.7 t = b2/sb2 t = 1.4/5.6 = 0.25 t = b3/sb3 t = 12.6/2.8 = 4.5 Find P values Go to t table at df=14, look for t values x1 < 0.05, x2 > 0.05, x3 < 0.05 The p-values for the first and third factors are less than .05, so they are significant

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% R-Sq(adj) = 1 - (1 - R^2)(n-1/n-p-1) n = 50, p =3 R-Sq(adj) = 1 - (1 - .8455)(50-1/50-3-1) R-Sq(adj) = .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 + B2x2 + ... + Bpxp + ε is called:

a multiple regression model.

The multiple regression equation based on the sample data, which has the form of yhat = 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, ε

Which of the following variables is categorical?

gender

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

increase by 6 units. Test it. yhat = 5 + 6x1 - 7x2 yhat = 5 + 6(1) - 7(1) yhat = 4 Increase x1 by 1 yhat = 5 + 6(2) - 7(1) yhat = 10 10 - 4 = increase by 6 units

A regression model between sales (yhat in $1,000) and unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function: yhat = 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 $3,000. The coefficient of the unit price (-3) indicates that if the unit price is increased by $1 (holding advertisement constant), sales are expected to decrease by $3,000. -3 (1) = -3 in thousands = decrease of $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, ε, 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 used 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 anaylsis

In a multiple regression model, the values of the error term, ε, 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 plane or surface, its graph is called a:

response surface

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

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

In 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 yhat = 5 + 6x1 - 7x2. Predict yhat when and x1 and x2. ????????

yhat = 31 yhat = 5 + 6x1 - 7x2 ?????????