Assignment 10

We went over everything you need for assignment ten last week, so here is some help. We won't be going over it this Thursday in Lab.

In one of my labs, I wasn't able to get to "r^2" (r -squared). The definition of r-squared is as follows:

"The percent variation in y, explained by x".

Realize that it is a percentage basically describing how much our x variable (explanatory) explains or describes our y variable (response). For example, Let's use house price versus house size again. You can probably imagine what this would look like (Draw it if it will help). House size is our explanatory variable and price is our response. It has a positive relationship because as house size increases, so does house price.

Now, let's say our r-value (correlation) for this is .8. To get r^2, we just square it. Thus, we get .64. r^2 is usually in a percentage, so we would say 64%.

According to the definition, (The percent variation in y, explained by x), this means "64% of variation in house price is explained by how big your house is".

This probably makes sense. A lot of how expensive our house is is because of the size. But the other 36% could be explained by location, schools nearby, property, newness, etc. This should help with problem 6.

Problem 7 is the weird one I told you about. I"ll step you through it. Remember, you'll never have to do this again.

You'll notice we have the variables "Sy and Sx" and "Y-bar and X-bar". Sx and x-bar refer to the standard deviation and mean of the x, or explanatory, variable. That means Sy and Y-Bar refer to the standard deviation and mean of y, or response, variable.

Looking at the problem, which is the explanatory and which is the response variable? Try to figure it out on your own first.



Did you get that the wife's height is the explanatory and the husband's height is the response? The clue here was that we were using the "regression line to predict the husbands height from the wife's height".

Knowing that, then it becomes easy. Sx=2.7 and x-bar=64. Sy=2.8 and y-bar=69.3. r=correlation coefficient, which is given.

Solve for b first, then plug it into the next equation.

For questions 9-12, make sure you follow the StatsCrunch instructions on Blackboard. They will help you produce an output that will make answering these questions easy.

Question 12 is asking about something called "extrapolation" which you should have learned in lecture. Extrapolation means trying to predict a y for an x outside of the range of your data. For example, let's use the example of credit hours versus hours of sleep at night.

Let's say we only collected data up until 15 credit hours. We could NOT use our line to predict someone who was taking 18 credit hours. Why not? Because we would not know what the regression line was doing after 15 credit hours.

Be careful on Question 14 - make sure you are talking about differences in the students not the environments.

Good Luck!
-Hillary