Take a look at the data below. X represents an Internet survey respondent’s rating of how satisfied they are with their Snapchat app and Y represents the respondent’s rating of how likely they would be to recommend the app to a friend.
a. Draw a scatter plot of the variables.
b. Using visual estimation, draw the line that appears to best fit the data.
c. What can you say about the relationship between satisfaction with the Snapchat app and the likelihood of recommending?
d. Use a protractor to measure the angle between the x-axis and the line you drew. What is it?
e. Find the cosine of the angle.
f. Now, enter the data into the software of your choice and conduct a simple regression predicting likelihood of recommending Snapchat. Interpret the results.
g. Also, using the software, compute the covariance and correlation between the two variables.
h. Compare the values of the correlation, the standardized regression coefficient, the covariance, and the unstandardized regression coefficient.
i. How close is the cosine of the angle to the correlation?
j. If the cosine is close to the correlation and standardized regression coefficient (which should be the same), then you visually estimated the simple regression with accuracy because the cosine of an angle is another way of expressing correlation. Comment on your accuracy.
