Question

Consider this scatter plot.

(a) How would you characterize the relationship between the hours spent on homework and the test

scores? Explain.


(b) Paul uses the function y = 8x + 42 to model the situation. What score does the model predict for 3 h

of homework?

Answer 1

a) For this case we can see on the y axis the test scores and on the x axis the hours of homework. And as we can see we have a proportional relationship, because when the hours of homework increase the test scores increases too. If we fit a lineal model between y and x we will see an slope positive and a correlation coefficient positive based on the data observed.

b)
`y = 8x +42`

And we want to predict the test score for x = 3hr of homework we just need to replace the value of x=3 in the linear model and we got:

`y = 8*3 +42= 24+42=66`

And that would be our predicted value for 3 h of homework

Explanation:

For this case we consider the scatter plot attached to solve the problem.

Part a

For this case we can see on the y axis the test scores and on the x axis the hours of homework. And as we can see we have a proportional relationship, because when the hours of homework increase the test scores increases too. If we fit a lineal model between y and x we will see an slope positive and a correlation coefficient positive based on the data observed.

Part b

Assuming the following linear model for the situation:

`y = 8x +42`

And we want to predict the test score for x = 3hr of homework we just need to replace the value of x=3 in the linear model and we got:

`y = 8*3 +42= 24+42=66`

And that would be our predicted value for 3 h of homework