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Chapter Seven

Problem 1) Look at the scatter plot below. Does it demonstrate a positive or negative correlation? Why?

Are there any outliers? What are they?

Answer: This scatter plot demonstrates a positive correlation because the values of Y increase with the increasing values of X with the correlation becoming stronger forming a positive slope. Yes there is an outlier. The second to the last data element is an outlier because it stands out from the rest of the data elements.

Problem 2) Look at the scatter plot below. Does it demonstrate a positive or negative correlation? Why?

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The relationship is negative. The increase in the number of calories lead to a decrease in the infant mortality rate.

Problem 4)

Bill is doing a project for you in the marketing department. In conducting his analysis regarding consumer behavior and a new product that has come out, he tells you the correlation between these two variables is 1.09. What is your response to this analysis?

Answer: The analysis indicates a significant positive relationship between the two variables. New products have a positive impact on consumer behavior.

Problem 5)

Judy has conducted an analysis for her supervisor. The results she obtained was a correlation coefficient that was negative 0.86. Judy is confused by this number and feels that because it is negative and not positive, is means that it is bad. You are here supervisor. How would you clarify this result for Judy regarding the meaning of the correlation?

Answer: A negative coefficient does not necessarily mean the figure is bad, it means that the relationship between the variables is inversely proportional. This means that an increase in one variable leads to a decrease for the other variable.

Problem 6)

Explain the statement, “correlation does not imply causality.”

Answer: This phrase is basically saying that the correlation between two variables does not always mean that one variable causes the other. However, correlation is not proof of existence of causation relationships.

Problem 7)

Using the best-fit line below for prediction, answer the following questions:

a) What would you predict the price of Product X in volume of 150 to be (approximately)?

Answer: 250

b) What would you predict the price of Product X in volume of 100 to be (approximately)?

Answer: 175

Problem 8)

You are interested in finding out if a student’s ACT score is a good predictor of their final college grade point average (GPA). You have obtained the following data and are going to conduct a regression analysis. Follow instructions on page 244 of your textbook under line of best fit to conduct this analysis?

ACT GPA

22.0 3.0

32.0 3.78

33.0 3.68

21.0 2.94

27.0 3.38

25.0 3.21

30.0 3.65

a) What is the R? What type of relationship does it indicate (strong/weak; positive/negative)?

Answer:

X Y XY XX

22 3 66 484

32 3.78 120.96 1024

33 3.68 121.44 1089

21 2.94 61.74 441

27 3.38 91.26 729

25 3.21 80.25 625

30 3.65 109.5 900

Regression: Y= b + mx

M= gradient

M= (NEXY – (EX)(EY))...

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