Q:

# A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table

Accepted Solution

A:
Remark
This is one of those cases where you are getting confused by a lot of numbers some of which you should not be concerned with. You are given y = ax + b.

You are told that the best fitting line has values of a = - 3.6 and b = 12.8.

All you need do is put that into the general equation and try different values for it.

So you have y = - 3.6 x + 12.8

Now Let's run a couple of numbers.
The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.

y = - 3.6(1) + 12.8
y = 9.2 which is not a bad result for x = 1

You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.

C
-0.998 = -3.6(1) + 12.8
This answer cannot work. We've already shown that x =1 will leave us close to 9Β  not -998 so C is incorrect.

B
y = 12.8x - 3.6
Let x = 1
y = 12.8(1) - 3.6
y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5

y= 12.8*5 - 3.6
y = 64 - 3.6 which is nowhere's near - 5. So B is wrong.

A
y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.

x = 3. y should come to somewhere near 2.
y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.
It is not close enough to 2 to be acceptable.