a Discuss the direction and strength of the association.
B
b What residual is furthest away from the x-axis?
C
c Substitute the volume of gas into the line of best fit.
D
d What volume does the line of best fit predict when the pressure is 8 atmospheres?
A
a See solution.
B
bGreatest residual: 2.3
Point: (2,12.45)
C
cTable of Values:
x
y
2.5
9.4
4.5
6.1
6.5
2.8
D
d It would not work well, see solution.
Practice makes perfect
a Let's first discuss the direction and strength of the line of best fit, and then we can analyze the slope.
Direction and strength
Examining the line of best fit, we notice that it has a negative slope and a correlation coefficient close to - 1. This tells us the association is strong. Also, an r-value of - 0.903 corresponds to an R-squared of (- 0.903)^2≈ 0.815. This means about 81.5 % of the high temperature the next day is explained by the high temperature on the previous day.
Slope
The slope is - 1.65, which means the volume of the gas decreases on average by 1.65 liters for every atmosphere the pressure increases.
b Examining the residual plot, we see that the greatest residual is about 2.3 when x=2 for oxygen. It corresponds to the point (2,12.45).
c Let's substitute 2.5, 4.5 and 6.5 instead of x and simplify.
x
13.51-1.65x
y
2.5
13.51-1.65( 2.5)
9.4
4.5
13.51-1.65( 4.5)
6.1
6.5
13.51-1.65( 6.5)
2.8
d When the pressure is greater than 8 atmospheres, the model dips below the x-axis, which would mean we have a negative volume. This is not possible, and therefore its predictive power is not good for more extreme pressures.
