Question

I Need Help With Statistics

Answer 1

Part A

There is a perfect positive correlation going on here, so r = +1 or simply r = 1. This is because all of the points are on the same straight line, and this line has a positive slope. Each time x goes up by 1, y goes up by 3. The slope is m = (change in y)/(change in x) = 3/1 = 3

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Part B

The slope is 3 as mentioned back in part A. Further confirmation can be shown if you pick any two points and use the slope formula m = (y2-y1)/(x2-x1). I'll use the first two points

m = (y2-y1)/(x2-x1)

m = (7-4)/(1-0)

m = 3/1

m = 3

Note how (x,y) = (0,4) is on the line so the y intercept is 4.

So we go from y = mx+b to y = 3x+4

Plug x = 0 into y = 3x+4 and you should get y = 4. Plug x = 1 into y = 3x+4 and you should get y = 7. Etc etc

The function that perfectly fits the data is y = 3x+4

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Part C

The slope is 3 tells us how fast the plant grows per day. In this case, it grows 3 centimeters per day. You can think of this as the unit rate.

The y intercept is the starting height of the plant, which is 4 cm. On day 0 (starting day) the plant is 4 cm tall. The y intercept is the point where the graph crosses the y axis as shown in the attached image below.