Question 9 (essay worth 10 points) (08.06a mc) the graph below shows the relationship between the number of months different students practiced baseball and the number of games they won: the title of the graph is baseball games. on x axis, the label is number of months of practice. on y axis, the label is number of games won. the scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. the points plotted on the graph are the ordered pairs 0, 1 and 1, 3 and 2, 5 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 14 and 8,17 and 9, 18 and 10,20. a straight line is drawn joining the ordered pairs 0, 1.8 and 2, 5.6 and 4, 9.2 and 6, 13 and 8, 16.5 and 10, 20.5. part a: what is the approximate y-intercept of the line of best fit and what does it represent? (5 points) part b: write the equation for the line of best fit in slope-intercept form and use it to predict the number of games that could be won after 13 months of practice. show your work and include the points used to calculate the slope. (5 points)

Wow. I'm answering because that looks like a pain to type in. You can just post a picture you know.

Given points (0, 1),...(10,20)

Given a line through (0, 1.8) ... (10, 20.5)

Presumably the line described is the best fit line. You've told us the y intercept (the value when x=0) is 1.8. I believe you.

1.8

What does it represent? The independent x is the number of months of practice. The dependent y is number of games won. The intercept of 1.8 says after zero months of practice we'll have won 1.8 games (on average). I know it's not clear exactly how that makes sense, but that's what it says.

Part B

For part B I'm tempted to show you how to do a real linear regression, but this is marked middle school so I better not.

Let's just take the first and last point. (0, 1), (10,20)

The line through those two points is

(10 - 0)(y - 1) = (20-1)(x-0)

10y - 10 = 19 x

10 y = 19x + 10

y = 1.9 x + 1

That's a bit different than the described best fit but we'll go with it. We got a slope of 1.9 and a y intercept of 1.

At x=13 we get

y = 1.9(13) + 1 = 25.7

25.7 wins after 13 months of practice predicted

A) I would say the y-intercept is 1. It represents when the baseball team first started playing.

B) I think they would win 26 games Because I'm gonna use 1,3 and 2,5 so we need to subtract the y's and x's so 2-1 is 1 and 5-3 is 2 so 1,2 so the slope is 2/1 two times 13 is 26 so they will win 26 times.