Exam 4
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