Bana SHSU Exam 4

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

False

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

increase by 25 pounds. 5(5)=25

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

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: ŷ = 77+8 x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

True 77+8(6) = 125

A regression analysis between sales (denoted by y) and advertising (denoted by x ) resulted in the following least squares line: ŷ = 77+8 x. This implies that:

as advertising increases by $5,000, sales are predicted to increase by $40,000.

In a regression problem, if the R-squared is 0.95, this means that:

95% of the variation in y can be explained by the variation in x.

In regression analysis, the coefficient of determination R2 measures the amount of variation in y that is:

explained by the variation in x.

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

1.0 when x = 1.0

In regression analysis, if the R-squared is 1.0, then:

the sum of squares for error must be 0.0

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

$8,800 4000+6(800) = 8800

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

A multiple regression model has the form: ŷ = 5.25 + 2 x 1 + 6 x 2 . As x 2 increases by five units, holding x 1 constant, then the value of y is predicted to increase by:

30 units 6(5) = 30

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

For the following multiple regression model: ŷ = 2 - 3 x 1 + 4 x 2 + 5 x 3, a unit increase in x 1, holding x 2 and x 3 constant, results in:

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

A confidence interval (as opposed to a prediction interval) is used to estimate the long-run average value of y.

False

In a multiple regression model, the value of the R-squared has to fall between

0 and +1.

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

True

A multiple regression model has the form ŷ = 8+ 3 x 1+ 5 x 2 - 4 x 3. As x 3 increases by one unit, with x 1 and x 2 held constant, the y on average is expected to:

decrease by 4 units.

There is more error in estimating a mean value of y as opposed to predicting an individual value of y.

True