1. ## Question about regression analysis (Q scanned in)

Hi
I have just completed A-level maths in 12 months, and am helping out one of my dad's friends at work, who needs to do a bit of maths as part of his apprenticeship course. Its a question about regression, and the formula
y= A + Bx. (Question 2 on attachment)

After inputting the two lines of data into my calculator, it returned values of 5.5575 for B, and 6.1957 for A. But when inputting the x value as 1.1, i.e. first value in the table, i got 12.308, rather than the 12.0 i was hoping for.

I then did the long version, calculating B manually and A manually, and got MINUS numbers, which obviously didn't fit.

I think its a small mistake along the way and i'm hoping someone can spot what i've done wrong because i can't!!

Thanks for reading, sorry its long-winded!!

2. You didn't make a mistaken. The linear regression line isn't going to fit your data points exactly. How can it? I mean if it did, then it would be a sure bet that you would be able to find an equation relating additive to miles (km) per gallon without even using a calculator.

Not sure how you calculated i t manually, however using the trusty TI, I got the same results that you did.

Do you know how to create a scatter plot on the TI? If you do a scatter plot, as well as the linear regression equation, you'll be able to see how things match up.

Is the 'TI' the calculator?? What does it stand for? I have a casio FX 83-ES calculator.

I've drawn a scatter graph with all the data points but that is just a tiny part of the question.

The main part is asking basically to find the equation, so are you saying that y = 6.1957 + 5.5575x is ok? And then for part a) if i input x as 0, then 6.1957 would be my answer?

(i manually calculated it using the formula to find B, which is
Exy - (n * mean of x * mean of y)
Ex^2 - (n * mean of x^2)

and A = mean of y - (B * mean of x)

But not sure they're asking for this, just the equation i think

4. Is the 'TI' the calculator?? What does it stand for? I have a casio FX 83-ES calculator.
Yes sorry. It's a TI-83. I kinda just assume thats what people use.

The main part is asking basically to find the equation, so are you saying that y = 6.1957 + 5.5575x is ok?
It is absolutely correct.

And then for part a) if i input x as 0, then 6.1957 would be my answer?
Yes. The equation is saying "If I put NO ADDITIVES in my fuel, then I should expect to get 6.1957 km/gallon. The validity of 6.1957 all depends on how strong a relationship there is between additive amount and km/gallon. There does some to be a positive-relationship between additive amount and mileage.

As such, a NEGATIVE value for A and B in this situation is for sure wrong, as you are essentially saying that without adding a fuel additive, your car would get MINUS miles per gallon, and not only that, but the MORE additives you add to your fuel, the WORSE mileage your car would go. A positive B and a negative A I can see, but not both being negative. That would be a hell of a car.

5. Thanks a lot dude. i was going insane trying to work it out.

Thanks!!!!!!