Question

Line of best fit?

Answer 1

Could someone please help me with this? I'm not sure what to do.

Answer 2

@campbell_st @fiji_tsunami @Kainui @KyanTheDoodle @LeilaJudeh @LelandP @Michele_Laino @Preetha

Answer 3

well the observed value would appear to come from the table...

so look at the x, y table for 8.1 and 10 and record the values in the 1st box...

next substitute 8.1 into the equation you have been given to get the predicted amount..

does that make sense?

Answer 4

if you have the equation of the best fit, just use that function to solve for the predicted amount \(f(x) = 0.5x + 22.45\) put the x-value into the x

Answer 5

the residual is the difference between the observed value and predicted value

Answer 6

Do you mind if I try it step-by-step and you tell me if I'm doing it correctly?

Answer 7

OKAY

Answer 8

let us pick one of the data

Answer 9

33.50 = 0.5(8.1)+22.45

Answer 10

for \(x=8.1 \)
\(y = f(x) = 0.5x + 22.45 \rightarrow f(8.1) = 0.5\times (8.1) + 22.45 \)

Answer 11

I multiplied 0.5 with 8.1 and added it to 22.45. I have 26.5

Answer 12

so that is the predicted value at x=8.1
x-value indicates the time in hours

Answer 13

so 26.5 hours?

Answer 14

did you multiply and add properly?

Answer 15

8.1x0.5=4.05 and adding 4.05 to 22.45 gives us 26.5

Answer 16

So our first answer is 26.5 hours?

Answer 17

okay then

Answer 18

what else would it be if not that value?

Answer 19

I do not understand the difference between predicted and observed.

Answer 20

I'm guessing predicting means what I think before solving the problem?

Answer 21

predicted value is the value you solved using the LINEAR FIT equation
OBSERVED would be what the actual graph or table tells you

Answer 22

Ohhh. So observed would be what the table says? So predicted would be 33.50, is that right?

Answer 23

no
PREDICTED is the 26.5
OBSERVED is what is in the table

Answer 24

I mixed it up, sorry. 33.50 is observed. Predicted is 26.5

Answer 25

What exactly is residual?

Answer 26

the difference between the OBSERVED and PREDICTED values

Answer 27

when we say DIFFERENCE, what mathematical operation do we use?

Answer 28

33.50-26.5

Answer 29

correct

Answer 30

7 :)

Answer 31

how it actually works is that if the OBSERVED value is higher than the PREDICTED value, we say that the predicted value is 7 below the observed value or -7 from the observed value

Answer 32

So for the answer in the residual value box, would I insert -7 or 7?

Answer 33

positive

Answer 34

Thank you very much.

Answer 35

there's no negative dollar unless it is a debit or debt
in statistics, a residual analysis, like I said before, if the predicted value is lower than the observed, then it is negative and if it is higher than the observed then it is positive
residual is indicated by letter "e"
so -e tells you that you predicted value is lower than the observed
+e tells you that the predicated value is higher than the observed

Answer 36

http://stattrek.com/videos/ap/lessons/regression/residual-analysis/video.html