Exam 4

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A regression analysis between sales and advertising resulted in the following least squares line: y = 4000 + 6x . This implies that if advertising is $800, then the predicted amount of sales (in dollars) is:

$8,800

Suppose you have the following results from a regression analysis:

(0.1755, 7.2205)

What is the 95% confidence interval for β1?

(0.1755, 7.2205)

The R-squared ranges from:

0.0 to 1.0

In the least squares regression line y = 3 - 2x , the predicted value of y equals

1.0 when x = 1.0

A multiple regression model involves 10 independent variables and 30 observations. Suppose we want to test at the 5% significance level whether one (not all) of the coefficients is equal to 0 (versus not equal to 0). The critical value will be...

2.093

In order to estimate with 95% confidence, the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

2.306

The regression line y= 3 + 2x has been fitted to the data points (4, 8), (2, 5), and (1, 2). The sum of the squared residuals will be: 22

22

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations, the numerator and denominator degrees of freedom for the critical value of F are, respectively

5 and 24

A multiple regression model has the form: ŷ = 5.25 + 2x1 + 6x2 . As x2 increases by one unit, holding x1 constant, then the value

6 units on average

A multiple regression model has the form: ŷ = 5.25 + 2x1 + 6x2 . As x2 increases by one unit,holding x1 constant, then the value

6 units on average

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

6.26

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

6.26

Question

Answer

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

F-test

A regression analysis between sales (in $) and advertising (in $) resulted in the following least-squares line: y = 60 + 5x . This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

False

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: y = 135 + 6x . This implies that if the height is increased by 10 inches, the weight is expected to increase by an average of 195 pounds.

False

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be

Narrower

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:

Narrower

Which of the following techniques is used to predict the value of one variable on the basis of other variables?

Regression analysis

Which of the following techniques is used to predict the value of one variable on the basis of other variables?

Regression analysis

Suppose you have the following results from a regression analysis: n = 32 b0 = 0.567 se(b0) = 1.365 b1 = 3.698 se(b1) = 1.725 R-squared = 0.76 What is your decision regarding the null hypothesis as to whether the dependent variable and the explanatory variable are related? (Use a 10% significance level.)

Reject H0

A multiple regression is called "multiple" because it has several explanatory variables

True

A simple linear regression equation is given by y = 5.25 + 3.8x . The point estimate of y when x = 4 is 20.45.

True

For the following multiple regression model: ŷ = 2 - 3x1 + 4x2 + 5x3, a unit increase in x1, holding x2 and x3 constant, results in:

a decrease of 3 units on average in the value of y

A regression analysis between sales (in $1,000) and advertising (in $1,000) resulted in the following least-squares line:Y = 80 + 5x This implies that

as advertising increases by $1,000, sales increases by $5,000

In the simple linear regression model, the slope represents the:

average change in y per unit change in x

In the simple linear regression model, the population parameters of the y-intercept and the slope are estimated, respectively, by:

b0 and b1

b0

b1

The coefficient of correlation is used to determine the strength and direction of the linear relationship

between x and y

For the multiple regression model: ŷ = 75 + 25x1 - 15x2 + 10x3, if x2 were to increase by 5, holding x1 and x3 constant, the value of y will:

decrease on average by 75

In regression analysis, the residuals represent the

difference between the actual y values and their predicted values

A multiple regression model has the form ŷ = 8+ 3x1+ 5x2 - 4x3. As x3 decreases by four units, with x1 and x2 held constant, then y on average is expected to:

increase by 16 units

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: Y = 120 +5x This implies that if the height is increased by 1 inch, the weight, on average, is expected to

increase by 5 pounds

A multiple regression model has:

more than one independent variable.

A multiple regression model has:

more than one independent variable.

In a multiple regression analysis involving k independent variables and n data points, the number of degrees of freedom associated with the sum of squares for error is:

n - k - 1

Testing whether the slope of the population regression line could be zero is equivalent to testing whether the:

population coefficient of correlation could be zero

The symbol for the sample coefficient of correlation is

r

The least squares method for determining the best fit minimizes the

sum of squares for error

The residual is defined as the difference between:

the actual value of y and the estimated value of y

Given the least squares regression line y = 5 -2x:

the relationship between x and y is negative

If the coefficient of correlation between x and y is close to 1.0, this indicates that

there may or may not be a causal relationship between x and y

In the simple linear regression model, the y-intercept represents the:

value of y when x = 0

In the simple linear regression model, the population parameters of the y-intercept and the slope are, respectively,

β0 and β1

In reference to the equation ŷ = -0.80 + 0.12x1+ 0.08x2 , the value 0.12 is the average change in y per unit change in x1, when x2 is held constant.

True

whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:

H 0 : 1 0

If the R-squared is 0.95, this means that 95% of the variation in the independent variable x can be explained by the y variable

False

If the R-squared is 0.95, this means that 95% of the y values were predicted correctly by the regression line.

False

If there is no linear relationship between two variables x and y, the R-squared must be −1.0.

False

In testing the significance of a multiple regression model with three independent variables, the null

False

A positive relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

True

The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level. This is because there is less error in estimating a mean value as opposed to predicting an individual value.

True

If an estimated regression line has a y-intercept of 10 and a slope of 4, then when x = 2 the actual value of y is

Unknown


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