BANA 2082 - Quiz 7.4 Web Assign PDF

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BANA 2082 - Quiz 7.4 Web Assign...

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1.) In publishing the results of some research work, the following values of the coefficient of determination were listed. Which one would appear to be incorrect?

Answer: -0.64

2.) Given the least squares regression line yˆ = -2.88 + 1.77x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Answer: +0.90

3.) If the sum of squares due to regression (SSR) is 60, which of the following must be true?

Answer: The total sum of squares (SST) is at least 60.

4.) For the values of the coefficient of determination listed below, which one implies the greatest value of SSR (regression sum of squares) given that SST = 500?

Answer: 0.95

5.) In a regression problem the following pairs of (x, y) are given: (2,1), (2,-1), (2,0), (2,-2) and (2,2). That indicates that the:

Answer: coefficient of correlation is 0.

6.) Correlation analysis is used to determine the:

Answer: strength of the relationship between x and y.

7.) All of the values of an independent variable equal the same number. Regressing a dependent variable on this independent variable will result in a coefficient of determination (r 2 ) of:

Answer: 0.0

8.) The value for SSE equals zero. This means that the coefficient of determination (r 2 ) must equal:

Answer: 1.0

9.) A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: yˆ = 75 +6x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is:

Answer: $123,000

10.) The following values are listed as coefficients of correlation (r). The one that indicates an inverse relationship between the two variables x and y is:

Answer: -0.8

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

Answer: can be any units

12.) regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained.

Yˆ = 12 + 1.8 x

n = 17 SSR = 225 SSE = 75

Sb1 = 0.2683

The t statistic for testing the significance of the slope is

Answer: 6.709

13.) Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained.

Yˆ = 12 + 1.8 x

n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683

The critical t value for testing the significance of the slope at 95% confidence is

Answer: 2.131

14.) In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

Answer: 0.6000

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

Answer: can be either negative or positive

16.) If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is

Answer: 0.80

17.) If the coefficient of correlation is 0.90, then the coefficient of determination

Answer: must be 0.81

18.) If the coefficient of correlation is a negative value, then the coefficient of determination

Answer: must be positive

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

Answer: the slope of the line must be positive

20.) The coefficient of correlation

Answer: is the square root of the coefficient of determination

21.) A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?

Answer: a positive correlation

22.) A researcher records the odometer reading and price for a group of used Hondas. What kind of correlation is likely to be obtained for these two variables?

Answer: a negative correlation

23.) For the linear equation Y = 2X - 3, which of the following points will not be on the line?

Answer: 3,0

24.) An analysis of variance is used to test the significance of a simple linear regression equation based on a sample of n = 20 individuals. What are the df values for the F-ratio?

Answer: 1, 18

25.) The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers. The correlation between amount of TV violent content and amount of violent behavior is an example of _______.

Answer: a positive correlation

26.) Which of the following statements are true regarding the simple linear regression model yi=β0+β1xi+εi ?

Answer: *****All of the above are true statements.

εi is a random error, or residual.

Incorrect Response yi is a value of the dependent variable (y) and xi is a value of the independent variable (x).

β1is the slope of the regression line.

β0is the y-intercept of the regression line.

27.) A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: yˆ = 120 + 5x. This implies that if the height is increased by 1 inch, the weight is expected to:

Answer: increase by 5 pounds.

28.) For a given value of x, the estimation interval for an individual y observation is called the:

Answer: prediction interval

29.) Another name for the residual term in a regression equation is:

Answer: random error

30.) Which of the following table values would be appropriate for a 95% confidence interval for the mean of y from a simple linear regression problem if the sample size is 7?

Answer: 2.571

31.) Regardless of the value of x, the standard deviation of the distribution of y values about the regression line is the same. This assumption of equal standard deviations about the regression line is called:

Answer: homoscedasticity.

32.) The vertical spread of the data points about the regression line is measured by the:

Answer: standard error of estimate

33.) If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation:

Answer: must be either 1.0 or -1.0

34.) In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

Answer: 2.306

35.) The residual is defined as the difference between the:

Answer: actual value of y and the estimated value of y.

36.) In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

Answer: 0.40

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

Answer: must have a positive slope

38.) The value of the coefficient of correlation (R)

Answer: can be equal to the value of the coefficient of determination (R2)

39.) In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is

Answer: 0.65

40.) If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Answer: 64%

41.) In simple linear regression analysis, which of the following is not true?

Answer: The F test and the t test may or may not yield the same conclusion.

42.) In regression analysis, the independent variable is

Answer: used to predict the dependent variable

43.) In a regression analysis, the variable that is being predicted

Answer: is the dependent variable

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

Yˆ = 500 + 4 X

Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

Answer: $900,000

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

Answer: the regression model

46.) If there is a positive correlation between X and Y, then the regression equation Y = b0 + b1X will have _____.

Answer: b1 > 0

47.) For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase?

Answer: 2 points

48.) Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

Answer: -0.90

49.) A linear regression equation has b1 = 3 and b0 = - 6. What is the predicted value of Y for X = 4?

Answer: 6

50.) A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables?

Answer: A correlation near zero

51.) In simple linear regression, the coefficient of correlation r and the least squares estimate b1 of the population slope β1:

Answer: must have the same sign

52.) In a regression problem, if the coefficient of determination is 0.90, this means that:

Answer: 90% of the variation in y can be explained by the regression line

53.) A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: yˆ = 80,000 + 5x. This implies that an:

Answer: increase of $1 in advertising is expected to result in an increase of $5,000 in sales.

54.) If the standard error of estimate sy.x = 18 and n = 10, then the error sum of squares, SSE, is:

Answer: 2592

55.) The regression line yˆ = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The residual sum of squares will be:

Answer: 22

56.) An indication of no linear relationship between two variables would be:

Answer: a coefficient of correlation of 0

57.) A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation

Yˆ = 60 - 8X

The above equation implies that an

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

58.) In a regression analysis, the regression equation is given by Yˆ = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is

Answer: -0.7

59.) In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

Answer: 0.65

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

Answer: least squares line

61.) Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained.

Yˆ = 80 + 6.2 X

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

Answer: $700,000

62.) If the coefficient of determination is 0.81, the coefficient of correlation

Answer: could be either + 0.9 or - 0.9

63.) In a regression and correlation analysis if r2 = 1, then

Answer: SSE must be equal to zero

64.) 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

Answer: 1

65.) In regression and correlation analysis, if SSE and SST are known, then with this information the

Answer: coefficient of determination can be computed

66.) SSE can never be

Answer: larger than SST

67.) What is indicated by a positive value for a correlation?

Answer: Increases in X tend to be accompanied by increases in Y

68.) For the regression equation, mc034-1.jpg = -2X + 6, what can be determined about the correlation between X and Y?

Answer: The correlation definitely will be negative.

69.) A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation?

Answer: r = 0.40

70.) It is possible for the coefficient of determination to be

Answer: less than one

71.) If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable

Answer: is 90%

72.) In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is

Answer: 0.0256

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

Yˆ = 500 + 4 X

Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

Answer: $900,000

74.) If the coefficient of correlation is -0.4, then the slope of the regression line

Answer: must be negative

75.) An analysis of variance is used to test the significance of a simple linear regression equation based on a sample of n = 20 individuals. What are the df values for the F-ratio?

Answer: 1, 18

76.) If two variables, x and y, have a strong linear relationship, then

Answer: there may or may not be any causal relationship between x and y

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

Answer: one dependent and one or more independent variables are related

78.) Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained.

Yˆ = 50 + 8 X

Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is

Answer: $1,300,000

79.) The following information regarding a dependent variable (Y) and an independent variable (X) is provided.

YX

42 31 44 63 85

SSE = 6 SST = 16

The coefficient of determination is

Answer: 0.625

80.) If there is a very strong correlation between two variables then the coefficient of determination must be

Answer: None of these alternatives is correct

81.) In the following estimated regression equation yˆ=b0+b1x

Answer: b1 is the slope

82.) 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.

Yˆ = 120 - 10 X

Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

Answer: decease by 20 units

83.) Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained.

Yˆ = 12 + 1.8 x

n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683

Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

Answer: 66,000

84.) A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation

Yˆ = 60 - 8X

The above equation implies that an

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

85.) In regression analysis, the variable that is being predicted is the

Answer: dependent variable

86.) A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation

Yˆ = 9 - 3X

The above equation implies that if the price is increased by $1, the demand is expected to

Answer: decrease by 3,000 units...