- A measure of goodness of fit for the estimated regression equation is the multiple coefficient of determination
- A multiple regression model has more than one independent variable
- A multiple regression model has the form y-hat = 7 + 2 x1 + 9 x2As x1 increase by 1 unit (holding x2 constant), y-hat is expected to increase by 2 units
- A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the least squares method
- A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a dummy variable
- As the goodness of fit for the estimated multiple regression equation increases the value of the multiple coefficient of determination increases
- Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 – 3×1 + 5×2. For this model SSR = 3500, SSE = 1500, and the sample size is 18.Refer to Exhibit 15-2. The coefficient of the unit price indicates that if the unit price is increased by $1 (holding advertising constant), sales are expected to decrease by $3,000
- Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 – 3×1 + 5×2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. The coefficient of x2 indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to increase by $5,000
- Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 – 3×1 + 5×2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. If we want to test for the significance of the regression model, the critical value of F using alpha = .05 3.68
- Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 – 3×1 + 5×2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2, the test statistic F is 17.5
- Exhibit 15-3. In a regression model involving 30 observations, the following estimated regression equation was obtained y-hat = 17 + 4×1 – 3×2 + 8×3 + 8×4. For this model SSR = 700 and SSE = 100. Refer to Exhibit 15-3. The computed F statistic for testing the significance of the above model is 43.75
- For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is 0.75
- If a qualitative variable has k levels, the # of dummy variables required is k – 1
- If the coefficient of correlation is a positive value, then the slope of the regression line must also be positive
- If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope
- If the coefficient of determination is equal to 1, then the coefficient of correlation can be either -1 or +1
- In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is 0.700
- In a multiple regression model, the error term ε is assumed to be normally distributed
- In a multiple regression model, the error term ε is assumed to be a random variable with a mean of zero
- In a multiple regression model, the variance of the error term ε is assumed to be the same for all values of the independent variable
- In a regression analysis if r2 = 1, then SSR = SST
- In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is 0.6000
- In a regression analysis if SSE = 500 and SSR = 300, then the coefficient of determination is 0.3750
- In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see a horizontal band of points centered near zero
- In multiple regression analysis there can be several independent variables, but only one dependent variable
- In multiple regression analysis, the correlation among the independent variables is termed multicollinearity
- In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are 3 and 43
- 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 14 and 240
- In regression analysis, an outlier is an observation whose residual is much larger than the rest of the residual values
- In regression analysis, the independent variable is used to predict the dependent variable
- In regression analysis, the response variable is the dependent variable
- In regression analysis, the variable that is being predicted is the dependent variable
- In simple linear regression, r2 is the coefficient of determination
- Larger values of r2 imply that the observations are more closely grouped about the least squares line
- Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. Y^ = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is $700,000
- The adjusted multiple coefficient of determination is adjusted for the number of independent variables
- The correct relationship between SST, SSR, and SSE is given by SSR = SST – SSE
- The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual
- The multiple coefficient of determination is SSR/SST
- The numerical value of the coefficient of determination can be larger or smaller than the coefficient of correlation
- The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination
- Which of the following is correct SST = SSR + SSE
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