b Slope shows the change in y when you move one unit in the positive horizontal direction.
C
c R-squared is the correlation coefficient raised to the power of 2.
D
d How deep is the well at the y-intercept?
E
e Substitute the depth of the wells in the function and simplify.
F
f Calculate the predicted value and add the residual.
G
g Is there a random scatter about the x-axis in the residual plot?
A
a See solution.
B
b See solution.
C
cR-squared: 0.86
Interpretation: See solution.
D
d See solution.
E
e $2567, $3593, and $4325
F
f $2930
G
g Yes, it is appropriate. See solution.
Practice makes perfect
a Examining the line of best fit, we see that it has a positive slope and a correlation coefficient close to 1. This means we have a strong correlation. We cannot identify any apparent outliers.
b By examining the line of best fit we can identify the slope.
y=1395+ 14.65x
The slope is 14.65, which means the cost of a well increases on average by $14.65 when the depth increases by 1 foot.
c We have been given the r-value. To find R-squared, we have to raise this number to the power of 2.
R^2 =0.929^2 ⇔ R^2 ≈ 0.86
An R-squared of 0.86 means that 86 % of the variability in the cost is explained by the well's depth.
d Examining the line of best fit, we can identify the y-intercept.
y= 1395+14.65x
The y-intercept is 1395. This means that if we want to build a well, there is a fixed fee of $1395 that must be paid.
e To estimate the cost of wells that are 80, 150, and 200 feet, we have to substitute these values into the function and simplify.
x
1395+14.65x
y
80
1395+14.65( 80)
2567
150
1395+14.65( 150)
3593
200
1395+14.65( 200)
4325
The predicted cost for the three different wells are $2567, $3593, and $4325.
f The residual is the actual value minus the predicted value. Therefore, if we know the residual we can calculate the actual cost by determining the predicted value and then add the residual.
