QUIZ#3 - Linear/Multiple Regression Study Sheet

39. Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation 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.

34. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. y= 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.

22. In a regression analysis, the coefficient of correlation is .16. The coefficient of determination in this situation is

.0256.

27. If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

64%.

14. A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ​ y = 30,000 + 4x

increase of $1 in advertising is associated with an increase of $4000 in sales.

21. In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is

.65 if b1 is positive.

2. In regression analysis, the error term ε is a random variable with a mean or expected value of

0

38. If the coefficient of determination is .90, the percentage of variation in the dependent variable explained by the variation in the independent variable is

TBD

57. The mathematical equation which has the form of E(y) = β0 + β1x1 + β2x2 + ... + βpxp relating the expected value of the dependent variable to the value of the independent variables is

a multiple regression equation.

58. The equation which has the form of E(y) = = b0 + b1x1 + b2x2 + ... + bpxp is

an estimated multiple regression equation.

9. In the following estimated regression equation = b0 + b1x,

b1 is the slope.

24. If the coefficient of determination is equal to 1, then the coefficient of correlation

can be either -1 or +1.

5. If the coefficient of determination is a positive value, then the coefficient of correlation

can be either positive or negative.

25. All the independent variables in a multiple regression analysis

can be either quantitative or qualitative or both. (I will explain)

13. The value of the coefficient of correlation (r)

can be equal to the value of the coefficient of determination (r2).

28. In regression analysis, if the independent variable is measured in pounds, the dependent variable

can be measured in any units.

35. In regression analysis, if the dependent variable is measured in dollars, the independent variable

can be measured in any units.

31. A least squares regression line

can be used to predict a value of y if the corresponding x value is given.

29. If there is a very weak correlation between two variables, then the coefficient of determination must be

closer or equal to zero.

10. The interval estimate of the mean value of y for a given value of x is the

confidence interval estimate.

26. Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. y= 120 - 10x Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

decease by 20 units.

36. A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: y= 9 - 3x The above equation implies that if the price is increased by $1, the demand is expected to

decrease by 3000 units.

. 60. In regression analysis, the response variable is the

dependent variable.

17. In regression analysis, the variable that is being predicted is the

dependent variable.

8. The model developed from sample data that has the form of = b0 + b1x is known as the

estimated regression equation.

33. A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: y= 60 - 8x The above equation implies that an

increase of $1 in price is associated with a decrease of $8000 in sales.

32. 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 these data

is 1.

4. The coefficient of correlation

is the square root of the r-square.

20. Larger values of r2 imply that the observations are more closely grouped about the

least squares line.

30. If the coefficient of correlation is -.4, then the slope of the regression line

must be negative.

15. Regression analysis is a statistical procedure for developing a mathematical equation that describes how

one dependent and one or more independent variables are related.

11. The interval estimate of an individual value of y for a given value of x is the

prediction interval estimate.

7. The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as the

regression equation.

6. In regression analysis, the model in the form y = ß0+ ß1x + ε is called the

regression model

37. If the coefficient of correlation is a positive value, then the

slope of the regression line must be positive.

16. In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then

the estimated regression line intercepts the positive y-axis.

18. The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

the regression model.

23. Correlation analysis is used to determine

the strength of the linear relationship between the dependent and the independent variables.

19. In regression analysis, the independent variable is

used to predict the dependent variable.

1. In simple linear regression, r2 is the​

​coefficient of determination.

12. 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.

50. A descriptive measure of the strength of linear association between two variables is the​

​correlation coefficient.

47. 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.