# Finding a linear model.

• September 26th 2011, 09:51 PM
AMV
Finding a linear model.
UPDATE: I got the answer, but I won't mess with the problem, in case others need it! I won't state the steps though, to stay in line with this sites cheating policy! (I believe that's right, anyways) (Nerd)

Gasoline mileage of automobiles is influenced by the horsepower of the automobile. Below is a table of the data, use the data table to answer the following question:

HP(x) 49|52|55|58|61|64|67
MPG(y) 65.4|56.5|46.0|49.2|40.3|39.4|36.1

QUESTION: Find a linear model that fits the data, round to four decimal places

Just an FYI, I know how to find linear models, but this one has gotten me completely confused. I know I need to start off with finding the slope, which I've tried, and continued to get wrong (the answer is in the back of the book). Does it have something to do with the fact that the first difference isn't equally separated? Please Help!!
• September 26th 2011, 09:52 PM
Prove It
Quote:

Originally Posted by AMV
Ok, I really need someone to explain this to me step-by-step, PLEASE! I have literally worked on this problem for three days!! Even just trying it would be appreciated!

Gasoline mileage of automobiles is influenced by the horsepower of the automobile. Below is a table of the data, use the data table to answer the following question:

HP(x) 49|52|55|58|61|64|67
MPG(y) 65.4|56.5|46.0|49.2|40.3|39.4|36.1

QUESTION: Find a linear model that fits the data, round to four decimal places

Just an FYI, I know how to find linear models, but this one has gotten me completely confused. I know I need to start off with finding the slope, which I've tried, and continued to get wrong (the answer is in the back of the book). Does it have something to do with the fact that the first difference isn't equally separated? Please Help!!

What are you allowed to use? Are you supposed to plot the points on a scatterplot then draw a line that fits by hand and find its equation? Or are you supposed to use linear regression to find a least-squares-line? Or some other method?
• September 26th 2011, 10:01 PM
AMV
I'm assuming that with this problem, linear regression. This is literally the only problem on our homework like this, so I really don't know what to do. But I know I must be missing a step and our book shows us how to use a graphing calculator, but my teacher wants us to do everything by hand, so I'm kind of stuck :\
• September 26th 2011, 10:30 PM
Prove It
Quote:

Originally Posted by AMV
I'm assuming that with this problem, linear regression. This is literally the only problem on our homework like this, so I really don't know what to do. But I know I must be missing a step and our book shows us how to use a graphing calculator, but my teacher wants us to do everything by hand, so I'm kind of stuck :\

The least squares line is given by $\displaystyle y - \bar{y} = b\left(x - \bar{x}\right)$, where $\displaystyle b = \frac{\sum{\left(x - \bar{x}\right)\left(y - \bar{y}\right)}}{\sum{\left(x - \bar{x}\right)^2}}$.
• September 26th 2011, 10:52 PM
AMV
Well, I tried that, and I probably did something wrong... I got -2.96 for slope again. Ugh...

The second part of the problem is to "Graph the model found in question 1 and the scatter plot of the data on the same axes. Discuss how good the model fits the data." If that helps at all..
• September 27th 2011, 11:47 AM
AMV
Re: Finding a linear model.
It took me a while but I think I figured it out! The missing step must have been the least squares part. I knew it was something little like that, that was throwing me off! (Giggle)

So, thanks for the least squares reminder!

Sometimes I just need to write the whole problem out to see what I'm doing wrong, and then...something just clicks. haha.

P.S. this site is great to use, especially when my library's math help center isn't open!