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
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
|
|
|
