Question

algebra 1 question please help!!
Medal + Fan

Answer 1

The table represents data collected on the time spent studying (in minutes) and the resulting test grade.

Time Spent Studying (min) 52 37 31 9 26 40 22 10 45 34 19 60
Grade on Test 95 84 72 58 77 86 72 43 90 81 62 98
Part 1: Create a scatter plot with the predicted line of best fit drawn on it. Determine the type of correlation (if any), and predict the model that will be used.
Part 2: Find the line of best fit for the data either by hand or using technology. Explain your method. Find the predicted score for each time listed in the table.
Part 3: Find the residuals, and decide if your model is a good fit. Explain your method. (If your model is not a good fit, complete Part 2 again with a different set of points or choose a different model.)

Answer 2

Im done with 1 and 2 only need 3

Answer 3

@alex1248191 can you please help?

Answer 4

can you help guys?

Answer 5

@campbell_st please help me....

Answer 6

well have you created a scatter plot...?

Answer 7

yes I have

Answer 8

I did it in excel, which makes it really easy.

looking at the data there is a strong positive correlation....

does that make sense...?

Answer 9

so did you get a correlation coefficient...?

Answer 10

is this it?
Positive correlation, and a linear model with a positive rate of progress will be used.

Answer 11

it is positive and linear... I had the correlation coefficient of r =0.947

the equation I got was

y = 0.9648x + 45.547

is that the same as you equation...?

Answer 12

no

Answer 13

what did you get...?

Answer 14

m=15x+45

Answer 15

here is my info

Answer 16

15 seems like a very significant slope.... for your line...?

Answer 17

yes this is for the line

Answer 18

so what about part 3...
Find the residuals, and decide if your model is a good fit. Explain your method. (If your model is not a good fit, complete Part 2 again with a different set of points or choose a different model.)

Answer 19

well you need to use the equation.... and look at the difference between the actual value and predicted value of the y values...

so using the equation you have substitute the 1st data point x = 52 and make a prediction about what you should be

so using you're equation it would be

\[y = 15 \times 52 + 45\]

which is 825.... that's why I think your slope is wrong...

but to give you the idea.... the residual is the actual score

when x = 52 the residual e = actual - predicted so e = 95 - 825

then if you do this for all the points... then the sum of the residuals sound be zero.

If you get zero as an answer, the line of best fit is an excellent predictor...

does that make sense...

Answer 20

oops should not sound

Answer 21

what?

Answer 22

ok...

your equation is y = 15x + 45

substitute the 1st x value from your table into your equation.... what do you get...?

Answer 23

52

Answer 24

substitute x = 52 into your equation so that you can get the predicted value

Answer 25

ok... 675

Answer 26

so now its actually e = 95 - 675

Answer 27

yes... so that is the residual...

you need to find all the residuals... and them sum them

the closer they are to zero... the better the line of best fit is at predicting...

or the more accurate the line is at describing the data.

Answer 28

so what should I do? :)

Answer 29

Ok... I think you need to recheck the equation of your regression line seeing the predicted values will be extremely large.... and the sum of the residuals will be large...

here is my graph and data

Answer 30

you can graph your residuals to see if there is a random pattern... and if there is you can say the linear regression model is a good fit.

Answer 31

ok... will do

Answer 32

you will also need the mean of the residuals... and show that line so you can see there is a a reasonably even spread of residuals above and below the mean.

hope it all makes sense...

Answer 33

hmm... somewhat

Answer 34

If you look at the last file I attached, the equation I used

y = 0.9648x + 45.547

seems too give quite reasonable values for the predictions...

Answer 35

ok I got the graph what now...

Answer 36

here is some notes from Shodor that explain residuals

http://www.shodor.org/interactivate/discussions/FindingResiduals/

Answer 37

ok so, is the answer to part 3:

y = 0.9648x + 45.547 and the residual is e = 95 - 675

Answer 38

well the equation is what you need....

and the plot of the residuals should look something like (its just an example)



an even spread above, below and on... would indicate a good regression line