hom 7

hom7.docx

1). In order to calculate the correlation coefficient, you will need to figure out the data (x and y) from the scatterplot (above). Here is a table to help you out. I've already put in all the values for time spent exercising (x) you will just need to find the values for y (happiness ratings); Hint: I’ve already done the first 3 people's scores for you: Participant # 1 spent 6.5 hours exercising and had a happiness rating of 10, Participant # 2 spent 6 hours exercising and had a happiness rating of 8).

After you've filled out the table, let's check to make sure you've got it right. For the person who spent 3.5 hours exercising what was their happiness rating?

Participant #	Time spent exercising	Happiness (Y)
1	6.5	10
2	6	8
3	5.5	7
4	5
5	5
6	4.5
7	4.5
8	4
9	3.5
10	3
11	2.5
12	2.5
13	2
14	1.5
15	1.5
16	1
17	1
18	0
19	0

Group of answer choices

Flag question: Question 2

Question 2

For the person who spent 1.5 hours exercising, what was their happiness rating (there are two possible answers here, you can just choose one answer and put that. Do NOT put both possible answers)

Flag question: Question 3

Question 3

Now it's time to calculate the correlation coefficient (Don't panic! It's not so bad!). Here is the formula to help you out! If you're struggling with this, be sure to read over the powerpoint from this week to help you figure out which values should go where. There is a really helpful table in that powerpoint that you should use to organize your data. Type your answer in the box below. Round to only three decimal places! If you put more than three decimal places in your answer, canvas may count your answer as wrong. Put only your value as your answer, do not put "r ="

ϒxy= n∑xy-∑x∑y

[n∑x2-₍∑x₎2][n∑y2-₍∑y₎2]

Flag question: Question 4

Question 4

Let's check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy, what was the value of ₍∑x₎2

Flag question: Question 5

Question 5

Let's check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy, what was the value of ∑xy?

Flag question: Question 6

Question 6

Let's check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy, what was the value of ∑x∑y?

Flag question: Question 7

Question 7

What does this correlation coefficient represent (in other words, how can you interpret this correlation coefficient)?

Group of answer choices

A causal relationship between time spent exercising and happiness

A strong negative correlation between time spent exercising and happiness

Zero correlation between time spent exercising and happiness

A weak negative correlation between time spent exercising and happiness

A weak positive correlation between time spent exercising and happiness

A strong positive correlation between time spent exercising and happiness

Flag question: Question 8

Question 8

What are three possible explanations for this correlational relationship? Since this is just a correlation, we can’t be sure if spending time exercising actually causes changes in your happiness. So, what are three possible other explanations that you can come up with for the correlation that you calculated (hint: think about possible "third variable" explanations for this correlation---what other variables or factors might be causing changes in both x and y that could explain this correlation?).

Happiness 6.5 6 5.5 5 5 4.5 4.5 4 3.5 3 2.5 2.5 2 1.5 1.5 1 1 0 0 10 8 7 6 5 5 4 4 4 5 6 5 3 6 3 4 3 5 2

Time Spent Exercising (hours/week)

Happiness