Question

Based on the data plotted, choose all that are correct.

A good line of best fit for the data is y = 15x + 55.

The data on the scatter plot shows a negative relationship.

If a student studies for 6 hours, they will receive a grade of about 100.

In general, the longer time spent studying, the higher the student's grade.

Answer 1

- If a student studies for 6 hours, they will receive a grade of about 100.

- In general, the longer time spent studying, the higher the student's grade.

Explanation:

Given

See attachment for plot

Required

Select all correct options

First, we determine the equation of best fit.

Pick two corresponding points on the plot

`(x_1,y_1) = (2,70)`

`(x_2,y_2) = (4,85)`

Calculate slope (m)

`m = (y_2 - y_1)/(x_2 -x_1)`

`m = (85 - 70)/(4-2)`

`m = (15)/(2)`

`m = 7.5`

The equation is then calculated as:

`y = m(x - x_1) + y_1`

This gives:

`y = 7.5(x - 2) + 70`

`y = 7.5x - 15 + 70`

`y = 7.5x +55`

The above represents the line of best fit.

By comparison, (a) is incorrect

We calculate the slope to be:

`m = 7.5`

Since the slope is positive, then the relationship is positive (b is incorrect)

Also, the positive slope implies that, as x increases, y also increase.

Hence, (d) is correct.

For (c), we substitute 6 for x in the calculated equation of best fit

`y = 7.5x +55`

`y = 7.5 * 6 + 55`

`y = 45 + 55`

`y = 100`

This shows that (c) is true because 6 hours of study gives a grade of 100