Correlation Coefficient

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Show your work for each problem.

1.
What does a correlation coefficient of indicate?
1. a)Perfect negative correlation
2. b)Perfect positive correlation
3. c)Moderate correlation
4. d)No correlation
2.
Which value of indicates the strongest correlation?
1. a)
2. b)
3. c)
4. d)
3.
If , what is ?
4.
A study finds that ice cream sales and drowning incidents both increase in summer. What can we conclude?
1. a)They are correlated, but ice cream doesn't cause drowning
2. b)Drowning causes people to buy ice cream
3. c)There is no relationship
4. d)Ice cream causes drowning
5.
A correlation of means what percentage of variance is explained? (Use )
6.
How would you describe a correlation of ?
1. a)Strong positive correlation
2. b)Weak positive correlation
3. c)Moderate positive correlation
4. d)Very strong positive correlation
7.
Given , , , , . Calculate .
8.
If the product , what is the denominator of the formula?
9.
For the data points : Calculate the means and then find .
10.
A researcher adds an outlier to their data and changes from to . What does this demonstrate?
1. a)Outliers don't affect
2. b) is sensitive to outliers
3. c) is always reliable
4. d)The data has no correlation
11.
Data: . Calculate the correlation coefficient step by step.
12.
A scatter plot shows points forming a perfect U-shape. What is the likely value of ?
1. a)Close to -1
2. b)Close to 0
3. c)Exactly 0.5
4. d)Close to 1
13.
If , what percentage of variance in is NOT explained by ?
14.
Compare two datasets: Dataset A has , Dataset B has . Which has stronger predictive power?
15.
What can you conclude if between two variables?
1. a)The data has errors
2. b)No relationship of any kind exists
3. c)No linear relationship exists
4. d)A perfect relationship exists
16.
Two stocks have . If Stock A drops 10%, approximately how much would you expect Stock B to change (in %)?