Assume that the variables x and y have a significant correlation.

Question

1.    Choose the best answer for each of the followings, and justify your answer with logical argument:                      

I. Given the equation of a regression line is y = 0.5x - 3, what is the best predicted value for y given x = 13? Assume that the variables x and y have a significant correlation. 

a) 35

b) 3.5

c) 0.35

Answer 1

Let's set up a hypothetical situation. You did a linear regression on some data. Let's say your "y" or variable of interest (dependent) is how many times a person clicks an ad for a shoe company based on the number of ads the company pays for on Facebook "x" (independent variable). The company collects data each month running different numbers of ads to see how many clicks they get.

Congrats! You ran the linear regression on your data in your respective computer software and got

y = 0.5 x - 3. What does this mean? It means for every ad "x", the number of clicks "y" goes up 0.5 units, or 0.5 clicks. This is not a perfect example, but if the company wanted to get at least 1 click, they must run at least 8 ads because the intercept (starting point) is -3. This is determined using algebra to solve the equations for the line for "y" (clicks), given x = 8 (ads).

y = 0.5 * 8 - 3

y = 1

Based on that, if the company runs 13 ads, how many clicks will they get?