SOLUTION: Consider the following data: X 4 6 8 9 19 Y 12 16 25 30 39 Which of the following statements is correct? a. The slope is -3.24. b. The intercept is 3.54. c. Whe

Question 1196550: Consider the following data:
X 4 6 8 9 19
Y 12 16 25 30 39
Which of the following statements is correct?

a.
The slope is -3.24.
b.
The intercept is 3.54.
c.
When X is 10, then the estimated sales will be 25.83
d.
Y = 3.54-3.24X
e.
Coefficient of determination is 0.9849.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Given Data

x	y
4	12
6	16
8	25
9	30
19	39

Use statistical software to compute the regression line equation.
I used GeoGebra.
The regression line is approximately y = 1.73x + 8.53 when rounding to two decimal places. This rules out choice D.

The equation y = 1.73x + 8.53 is in the form y = mx+b
m = 1.73 = slope
b = 8.53 = y intercept
These facts rule out choices A and B

Use software to compute the correlation coefficient r to get
r = 0.92488
which is approximate

Square that value to get
r = 0.92488
r^2 = (0.92488)^2
r^2 = 0.8554030144
r^2 = 0.8554
The coefficient of determination is approximately 0.8554
This rules out choice E.

So far we have eliminated: A, B, D and E

Let's plug in x = 10 into the regression equation
y = 1.73x + 8.53
y = 1.73*10 + 8.53
y = 25.83
This matches what choice C is showing.

Answer: C) When X is 10, the estimated sales will be 25.83

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