Question

Sophie's math teacher plots student grades on their weekly quizzes against the

number of hours they say they study on the pair of coordinate axes and then draws
the line of best fit. Based on the line of best fit, what quiz score should someone who
studied 5 hours expect?

Answer 1

To predict the quiz score for someone who studied 5 hours, substitute the value of x into the equation and solve for y.

Step-by-step explanation:

The equation ŷ = 72.5 + 2.8x represents the line of best fit in this scenario. To predict the quiz score for someone who studied 5 hours, you can substitute the value of x (number of hours studied) into the equation and solve for ŷ (quiz score). In this case, the calculation would be ŷ = 72.5 + 2.8(5) = 72.5 + 14 = 86.5.

Answer 2

Answer: 92

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Step-by-step explanation:

The line of best fit here is y = 6x+62

• m = 6 = slope
• b = 62 = y intercept

We started at (0,62) and go up 6 units and to the right 1 unit each time we move along this line.

If we tried something like x = 1, then,

y = 6x+62

y = 6*1+62

y = 6+62

y = 68

Meaning that someone spending 1 hour per week doing homework would lead to an estimated score of 68. This matches what the graph shows, and it helps confirm we have the correct regression line equation.

Let's now plug in x = 5

y = 6x+62

y = 6*5+62

y = 30+62

y = 92

Someone doing 5 hours of homework per week is estimated to get a score of about 92.