Question

The scatter plot below shows one class of Spanish students' time spent studying for their final versus the grade that they earned in the final. What grade would you predict for a student who studied for 105 minutes?

Answer 1

If you made a line of best fit, then the score would most likely be 95.

Answer 2

The predicted grads for a student who studied for 105 minutes is 94.

Explanation:

From the given figure the scatter points are (0,55), (0,65), (15,60), (15,65), (15,80),(30,55), (30,70), (30,80), (45,75), (45,80), (45,85), (60,80), (60,90), (60,95), (75,85), (75,90), (90,85), (90,95), (90,100), (120,80), (120, 95), (120,100).

The equation of best fit line is

`y=ax+b` ... (1)

where, a is slope and b is initial value.

`a=\frac{\sum_(i=1)^nx_iy_i-n\overline{x}\overline{y}}{\sum_(i=1)^nx_i^2-n\overline{x}^2}`

`b=\overline{y}-b\overline{x}`

Using graphing calculator we get,

`a\approx 0.2835`

`b\approx 64.3775`

Substitute the value of a and b in equation (1).

`y=0.2835x+64.3775`

Substitute x=105 in the above equation to find the predicted grads for a student who studied for 105 minutes.

`y=0.2835(105)+64.3775`

`y=94.145`

`y\approx 94`

Therefore the predicted grads for a student who studied for 105 minutes is 94.