To predict the value of the dependent variable of our interest (y) for the given
ID: 3217626 • Letter: T
Question
To predict the value of the dependent variable of our interest (y) for the given, specific values of the independent variables (the x-variables) using a multiple regression model, we substitute the values of the x-variables into the multiple regression equation and solve for the value of y. The resulting value of y is __________.
a point estimate of y
a confidence interval of the average value of y
a prediction interval of for a single value of y
an exact forecast of y
The regression coefficients of the independent variables (the x-variables) in a multiple regression model are referred to as __________.
full regression coefficients
partial regression coefficients
expanded regression coefficients
extended regression coefficients
In a multiple regression analysis the numerical value of the adjusted R2 is __________.
always less than that of the coefficient of multiple determination (R2)
always greater than that of the coefficient of multiple determination (R2)
never less than that of the coefficient of multiple determination (R2)
always equal to that of the coefficient of multiple determination (R2)
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares error (SSE) = 3000. The standard error of estimate (se) is __________.
12.25
150
20
11.96
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares error (SSE) = 3000. The coefficient of multiple determination (R2) is __________.
0.76
1.32
0.24
0.58
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares regression (SSR) = 9500. The number of degrees of freedom for the residual error is __________.
23
22
21
20
As n, the number of observations in the data set increases the gap between R2 and adjusted R2 ____________________________.
decreases
gets multiplied by n
increases
gets divided by n
remains the same
The adjusted R2 accounts for ___________________________________.
the number of observations
the number of independent variables in the model
the number of dependent variables in the model
the number of the outliers in the data set
the number of total degrees of freedom
The range for the coefficient of multiple determination is _______________.
– infinity to + infinity
– infinity to 0
0 to + infinity
0 to +1
A measure of goodness of fit for a multiple regression model is _____________.
mean square due to regression
coefficient of multiple determination
t-statistic
mean square due to error
Which of the following is not an admissible value for the coefficient of determination?
0
0.5
1.0
1.5
When additional independent variables are added to a simple linear regression, the coefficient of determination, R2 may __________.
increase or stay the same
become negative
decrease or stay the same
stay the same
To test if an individual B coefficient in the population multiple regression model is significantly different from zero, a hypothesis test is conducted on the corresponding bi coefficient in the regression equation developed using sample data. This test is a __________.
nonparametric test
F-test
t-test
z-test
The test statistic used to test the overall significance of a multiple regression model, the null hypothesis that each one the beta-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that at least one the beta-coefficients of the x-variables in the model is zero, is the __________.
F value from the F-distribution tables
2 statistic
t statistic
F value calculated as mean square regression divided by mean square error
In testing the overall significance of a multiple regression model, the null hypothesis that each one the beta-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that __________.
each one of the beta-coefficients of the x-variables in the model is zero
at least one of the beta-coefficients of the x-variables in the model is zero
each one of the beta-coefficients of the x-variables in the model is > zero
at least two of the beta-coefficients of the x-variables in the model is zero
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. The regression coefficient of x1 suggests this: __________.
The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the home if the age of the home were held constant
The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home with the age of the home allowed to vary
The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home if the age of the home were held constant
The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the home for homes of different ages
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________.
$205.00
$205,000.00
$200,000.00
$255,000.00
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. The regression coefficient of x2 suggests this: __________.
If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted increase of $2500 in the price of the homes
Whatever be the square feet area of the living space, a 1 year increase in the age of the homes will result in a predicted increase of $2500 in the price of the homes
If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted drop of $2500 in the price of the homes
Whatever be the square feet area of the living space, a 1 year increase in the age of the homes will result in a predicted drop of $2500 in the price of the homes
Explanation / Answer
Answer:
To predict the value of the dependent variable of our interest (y) for the given, specific values of the independent variables (the x-variables) using a multiple regression model, we substitute the values of the x-variables into the multiple regression equation and solve for the value of y. The resulting value of y is __________.
a point estimate of y
The regression coefficients of the independent variables (the x-variables) in a multiple regression model are referred to as __________.
partial regression coefficients
In a multiple regression analysis the numerical value of the adjusted R2 is __________.
always less than that of the coefficient of multiple determination (R2)
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares error (SSE) = 3000. The standard error of estimate (se) is __________.
12.25
Sqrt(3000/20)=12.247
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares error (SSE) = 3000. The coefficient of multiple determination (R2) is __________.
0.76
R square = 9500/12500 =0.76
In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares regression (SSR) = 9500. The number of degrees of freedom for the residual error is __________.
20
As n, the number of observations in the data set increases the gap between R2 and adjusted R2 ____________________________.
decreases
The adjusted R2 accounts for ___________________________________.
the number of independent variables in the model
The range for the coefficient of multiple determination is _______________.
0 to +1
A measure of goodness of fit for a multiple regression model is _____________.
coefficient of multiple determination
Which of the following is not an admissible value for the coefficient of determination?
1.5
When additional independent variables are added to a simple linear regression, the coefficient of determination, R2 may __________.
increase or stay the same
To test if an individual B coefficient in the population multiple regression model is significantly different from zero, a hypothesis test is conducted on the corresponding bi coefficient in the regression equation developed using sample data. This test is a __________.
t-test
The test statistic used to test the overall significance of a multiple regression model, the null hypothesis that each one the beta-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that at least one the beta-coefficients of the x-variables in the model is zero, is the __________.
F value calculated as mean square regression divided by mean square error
In testing the overall significance of a multiple regression model, the null hypothesis that each one the beta-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that __________.
at least one of the beta-coefficients of the x-variables in the model is zero
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. The regression coefficient of x1 suggests this: __________.
The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the home if the age of the home were held constant
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________.
$205,000.00
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. The regression coefficient of x2 suggests this: __________.
If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted drop of $2500 in the price of the homes
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