c The residual is the actual value minus the predicted value.
D
d The correlation coefficient is the r-value.
E
e Consider the slope, r-value, and R-squared.
A
aEquation: y=3.97x+110
Scatterplot:
B
b 281 watts
C
c 12
D
d r≈ 0.517
Interpretation: Moderate positive association
E
e See solution.
Practice makes perfect
a To make a linear regression of the temperature and attendance, we first have to enter the values into lists. Push STAT, choose Edit, and then enter the values in the first two columns.
To view the linear regression analysis of the dataset, push STAT, scroll right to view the CALC options, and then choose the fourth option in the list, LinReg.
The linear regression is y=3.97x+110. Let's create a scatterplot and sketch the graph.
b By substituting x=43 in the model, we can calculate the predicted power of the cyclist.
c The residual is the actual value minus the predicted value. From the exercise we know that the actual value is 293, and from Part B we know that the predicted value is 281. With this information, we can calculate the residual.
residual= 293- 281=12
d In Part A we calculated the correlation coefficient to be r≈ 0.517. This means the correlation coefficient is positive but not very strong, because it is not close to 1.
e Examining the linear regression, we notice that it has a positive slope and a correlation coefficient that is 0.517. This tells us that the association is not very strong. Also, the R-squared is 0.267, which means about 26.7 % of the variability in power is explained by the aerobic capacity.
