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Bus Stats 205

Quiz 8

Scatterplots, Correlation and Regression

Multiple Choice. Choose the one alternative that best completes the statement or answers the question

1. Suppose you were to collect data for the pair of given variables in order to form a scatterplot. Determine if each variable is independent/explanatory, dependent/response or whether it could be both.

Profits Levels for the year and Corporate Pay Bonus Rates for the year

A) Profit Levels for the year – independent/explanatory

Corporate Pa Bonus Rates for the year – dependent/response

B) Profit Levels for the year – dependent/response

Corporate Pa Bonus Rates for the year – independent/explanatory

C) Profit Levels for the year – either one

Corporate Pa Bonus Rates for the year – either one

Determine whether the scatterplot shows any association, what direction, if it is linear or not, and how strong is the association. Choose the MOST COMPLETE ANSWER THAT IS STILL A CORRECT ANSWER. Most complete being the answer that will give the greatest description. Start with direction, then linear, then strength.

A) Negative association, Linear association

B) Linear association, strong association

C) Positive association, non-linear association, moderately strong association

D) Positive association, linear association, moderately strong association

A) Negative association, Linear association, weak association

B) Negative association

C) Linear association, moderately strong association

D) Positive association, linear association, moderately strong association

4. Determine if the residual plot is appropriate for a linear model to fit the data. Is there a violation of the Equal Variance Condition or not?

A) The model is appropriate, no pattern exist

B) The model is not appropriate. There is a non-linear pattern

C) The model may not be appropriate. A fan tail pattern exists

5. Which of the points on the scatterplot would be probable outliers?

A) Points A, C, and E

B) Points A, B, and D

C) Points A, D, and E

D) Points A and C

6. A regression was run on the variables, “Life Expectancy” and “Computer Ownership” for several nations. Stated below are the regression equation, the “r” and the “r2” from the regression test. What is the best conclusion to draw from analysis? (First: Spurious vs. True relationship, then the reason if a true relationship exists.

Regression Equation: ŷ = 69.701 + 0.0254x (Y = Years of Life Expectancy; X = Computer per 1000

“r” = .9574

“r2” = .9166

A) Computer ownership promotes health and long life, probably due to the greater access that computer owners have to health information on the internet.

B) Persons who live longer buy more computers over the course of their longer lives.

C) Although the “r” and “r2” are strong, computer ownership probably does not promote longevity. Instead national per capita wealth is a lurking variable that drives bot life expectancy and computer ownership.

D) Clearly, there is some as-yet unknown health benefit associated with using computers.

SHORT ANSWER: Give a written answer to the following questions

Using the graph below, answer questions 7 – 10. The graph has wins a year on the y-axis and millions of dollars spent on salary

Wins

Millions of $

“r2” = .94

Variable	Values
Intercept	0.81
Slope	7.65

7. Is a linear model appropriate in this case, yes or no; and why? (3pts)

8. Interpret the meaning of the “r2” value in the context of the two variables. (3pts)

9. State what the correlation value (‘r”) would be between the variables. (2pts)

10. State the linear equation by using the data provided in the box above. (2pts)

11. Create and solve your own original Regression problem using 2 quantitative variables in StatCrunch. You must have computer print outs for steps 2, 4 and 5. This problem must start from raw data; a good place to get this data is from your survey data if you have it; otherwise you will have to create the data. If outliers exist, you must run with and without outliers.

1. State your Problem (3pts)

2. Input and Visualize your data (Scatterplot) (3pts)

3. Check the Association and comment on each aspect (5pts)

Direction

Form

Strength

Outliers

Trend

4. Check the Conditions (5pts)

Random

Linear

Equal Variance

Nearly Normal

Outlier

5. Set up and run your test (8pts)

Run the Regression

Print Out should include

Regression Boxes

Scatterplot with the Regression Line

Histogram of Residuals

Residual Scatterplot

6. State your Conclusions (6pts)

Conclusion should discuss:

“r”, “r2”, Slope of the regression, p-value and if any outliers exist

(You MUST run again if outliers exist)