- A data point (observation) that does not fit the trend shown by the remaining data is called a (an) narrower
- A least squares regression line may be used to predict a value of y if the corresponding x value is given
- A measure of the strength of the relationship between two variables is the correlation coefficient
- 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 regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation
y hat = 9 – 3x
The above equation implies that if the price is increased by $1, the demand is expected to decrease by 3,000 units - A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation
= 9 − 3x
The above equation implies that if the price is increased by $1, the demand is expected to decrease by 3,000 units - A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation
y hat = 50,000 – 8x
The above equation implies that an increase of $1 in price is associated with a decrease of $8000 in sales - A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation
= 50,000 − 8x increase of $1 in price is associated with a decrease of $8000 in sales - A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation
= 50,000 + 6x
The above equation implies that an increase of $1 in advertising is associated with an increase of $6,000 in sales - A term that means the same as the term “population” in an ANOVA procedure is Treatment
- An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are 4 and 95
- An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are 3 and 16
- An observation that has a strong effect on the regression results is called a (an) influential observation
- Application of the least squares method results in values of the y intercept and the slope that minimizes the sum of the squared deviations between the observed values of the dependent variable and the predicted values of the dependent variable
- As the goodness of fit for the estimated regression equation increases the value of the coefficient of determination increases
- Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be narrower
- Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be narrower
- If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is .6
- If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is 1
- If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation is 16%
- If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation is 16%
- If the coefficient of correlation is a negative value, then the coefficient of determination must be positive
- 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 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
- If the coefficient of determination is equal to 1, then the coefficient of correlation can be either -1 or +1
- If there is a very strong correlation between two variables, then the coefficient of correlation must be can be either -1 or +1
- If two variables, x and y, have a strong linear relationship, then there may or may not be any causal relationship between x and y
- In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided.
SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square) 50.00 - In a regression analysis if r2 = 1, then SSR = SST
- In a regression analysis if r2 = 1, then SSE must be equal to zero
- 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 .3750
- In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is 0.65
- In a regression analysis, the variable that is being predicted is the dependent variable
- In a regression analysis, the variable that is being predicted is the dependent variable
- 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 an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is 40
- In multiple regression analysis, there can be several independent variables, but only one dependent variable
- In regression analysis if the dependent variable is measured in dollars, the independent variable can be any units
- In regression analysis, the independent variable is used to predict the dependent variable
- In regression analysis, the variable that is being predicted is the dependent variable
- In regression analysis, which of the following is not a required assumption about the error term ε? All are required assumptions about the error term
- In regression and correlation analysis, if SSE and SST are known, then with this information the coefficient of determination can be computed
- In simple linear regression analysis, which of the following is not true? The F test and the t test may or may not yield the same results.
- In simple linear regression, r2 is the coefficient of determination
- In simple linear regression, r2 is the coefficient of determination
- It is possible for the coefficient of determination to be less than one
- Larger values of r2 imply that the observations are more closely grouped about the least squares line
- Larger values of r2 imply that the observations are more closely grouped about the least squares line
- Regression analysis is a statistical procedure for developing a mathematical equation that describes how one dependent and one or more independent variables are related
- Regression analysis is a statistical procedure for developing a mathematical equation that describes how one dependent and one or more independent variables are related
- Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained.
y hat = 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 - Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained.
= 80 + 6.2x $700,000 - Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.
y hat = 500 + 4x
Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is $900,000 - Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.
= 500 + 4x $900,000 - simple linear regression EQUATION y(hat)= Bo + B1x
- Simple linear regression model y= Bo + B1x + E
- SSE can never be larger than SST
- The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual
- The equation that describes how the dependent variable (y) is related to the independent variable (x) is called the regression model
- The interval estimate of the mean value of y for a given value of x is the confidence interval
- The least squares criterion is min
- 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
- The required condition for using an ANOVA procedure on data from several populations is that the Sampled populations have equal variances
- Which of the following is correct? SST = SSR + SSE
- Which of the following is not a required assumption for the analysis of variance? Populations have equal means.
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