Exam 15: Multiple Regression

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error 12.924 4.425 -3.682 2.630 45.216 12.560 Analysis of Variance Source of Degrees of Sum of Mean Variation Freedom Squares Square F Carry out the test to determine if there is a relationship among the variables at the 5% level.The null hypothesis should

In multiple regression analysis, the correlation among the independent variables is termed

A part of the results obtained from a multiple regression analysis is shown below. $\text { ANOVA }$ df SS MS F Regression 384 48 Error 20 total 704 ​ a. How many independent variables were involved in this model? b. How many observations were involved? c. Determine the F statistic.

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model, SSR = 700 and SSE = 100.At the 5% level,

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error 12.924 4.425 -3.682 2.630 45.216 12.560 Analysis of Variance Source of Degrees of Sum of Mean Variation Freedom Squares Square F The F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

The following estimated regression equation has been proposed to predict monthly sales at a shoe store. ​ $\hat { y } = 40 - 3 x _ { 1 } + 12 x _ { 2 } + 10 x _ { 3 }$ where = competitor's previous month's sales (in \ 1000 ) = store's previous month's sales (in \ 1000 ) =1 if radio advertising was used; 0 otherwise = estimated sales (in \ 1000 s) a. Predict sales (in dollars) for the shoe store if the competitor's previous month's sales were $9000, the store's previous month's sales were $30,000, and no radio advertisements were run. b. Predict sales (in dollars) for the shoe store if the competitor's previous month's sales were $9000, the store's previous month's sales were $30,000, and 10 radio advertisements were run.

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). $\hat { y }$ = 30 + .7x₁ + 3x₂ Also provided are SST = 1200 and SSE = 384.The estimated income (in $) of a 30-year-old male is

The numerical value of the coefficient of determination.

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165 SSE = 60 ​ If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age (x₁ in years), level of education (x₂ ranging from 1 to 5), and the individual's gender (x₃ where 0 = female and 1 = male).The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficients Standard Error 0.625 0.094 0.921 0.190 -0.510 0.920 ANOVA df SS MS F Regression 84 Error 112 ​ a. Compute the multiple coefficient of determination. b. Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., x₂) is significantly different from zero. Let α = .05. c. At α = .05, perform an F test and determine whether or not the regression model is significant. d. As you note, the coefficient of x₃ is -.510. Fully interpret the meaning of this coefficient.

The ratio of MSR to MSE yields

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model, SSR = 700 and SSE = 100.The computed F statistic for testing the significance of the above model is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃ For this model, SSR = 600 and SSE = 400.The multiple coefficient of determination for the above model is

A regression model involved 5 independent variables and 136 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240.The multiple coefficient of determination is

A regression analysis involved 17 independent variables and 697 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have​

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: $\hat { y }$ = 7 - 3x₁ + 5x₂ For this model, SSR = 3500, SSE = 1500, and the sample size is 18.The multiple coefficient of determination for this problem is?