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AIM 2: Define and interpret the results of a scattegram.

1、Which of the following statements regarding scatter plots is most accurate? Scatter plots:

A) are used to examine the third moment of a distribution (skewness).

B) are used to examine the fourth moment of a distribution (kurtosis).

C) illustrate the relationship between two variables.

D) illustrate the scatterings of a single variable.

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The correct answer is C

A scatter plot is a collection of points on a graph where each point represents the values of two variables. They are used to examine the relationship between two variables.

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2、If the correlation between two variables is ?1.0, the scatter plot would appear along a:

A) straight line running from southwest to northeast.

B) a curved line centered in the scatter plot. 

C) a curved line running from southwest to northeast. 

D) straight line running from northwest to southeast.

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The correct answer is D

If the correlation is ?1.0, then higher values of the y-variable will be associated with lower values of the x-variable. The points would lie on a straight line running from northwest to southeast.

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3、In the scatter plot below, the correlation between the return on stock A and the market index is:

 

 [attach]13871[/attach]

A)    negative.

B)    positive.

C)   zero.

D)   not discernable using the scatter plot.

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The correct answer is B

In the scatter plot, higher values of the return on stock A are associated with higher values of the return on the market, i.e. a positive correlation between the two variables.

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AIM 3: Define and interpret the population regression function, regression coefficients, parameters, slope and the intercept.

1、Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R2 value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm’s sales during the following period does the regression model predict?

A) +0.72%.

B) +1.00%.

C) +0.65%.

D) +0.10%.

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The correct answer is B

The slope of the regression represents the linear relationship between the independent variable (the percent change in sales people) and the dependent variable, while the intercept represents the predicted value of the dependent variable if the independent variable is equal to zero. In this case, the percentage change in sales is equal to: 0.72(0) + 0.01 = +0.01.

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2、In the estimated regression equation Y = 0.78 - 1.5 X, which of the following is least accurate when interpreting the slope coefficient?

A) If the value of X is zero, the value of Y will be -1.5.

B) The dependent variable declines by -1.5 units if X increases by 1 unit.

C) The dependent variable increases by 1.5 units if X decreases by 1 unit.

D) -1.5 is the elasticity of Y with respect to X.

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The correct answer is A

The slope represents the change in the dependent variable for a one-unit change in the independent variable. If the value of X is zero, the value of Y will be equal to the intercept, in this case, 0.78.