c Is it colder or warmer in the northern hemisphere? How will that affect the look of your scatter plot?
A
a y=-0.5x+78.7, see solution.
B
b 65.7^(∘) F, see solution.
C
c See solution.
Practice makes perfect
a To find the line of best fit, we have to perform a linear regression. There are a few steps that are necessary in order to instruct the calculator to do a linear regression.
Enter Data Set into Lists
The first step is to enter the data points in the calculator. We can do this by pressing STAT and then choose the first alternative, Edit, in the menu that is presented to us.
Having done this, we will see a number of columns marked L1, L2, and L3.
Using the keypad, we enter our data set into the first two lists. The first lists holds the latitude, and the second list the average temperature.
Calculate Linear Regression
Once the values are entered, we can perform a linear regression. Press STAT and then use the keypad to choose the menu CALC. Here you have all available types of regressions the calculator can carry out.
By choosing the fourth option, LinReg ax+b, the calculator calculate a linear regression on our data set.
The linear regression is y=-0.5x+78.7. A slope of - 0.5 means that for every 1 degree that the latitude increases, the average temperature falls by 0.5^(∘) Fahrenheit.
b To estimate the average temperature of Piggs Peak, we substitute the latitude of this city into our line of best fit and calculate the corresponding y-value.
The average temperature in Piggs Peak is about 65.7^(∘). This is not far of from 65.3^(∘) which is the actual temperature of Piggs Peak. Notice that the line of best fit only gives approximate answers. Thus, for each predicted value, one can expect the actual value to be slightly off.
c To make a scatter plot of the data showing the average temperature of cities in the southern hemisphere, press 2nd and then Y= and choose plot 1. In plot 1, you turn on the scatter plot, choose L1 and L2 as your x- and y-lists as well as an appropriate mark for the data points.
Before pressing graph, you might want to change the Window so it fits your data. To do that you press WINDOW.
Finally, by pressing GRAPH we can plot our values.
If we did a similar scatter plot for the northern hemisphere, it is safe to assume that we would see a negative correlation between the latitude and average temperature as well. However, the scatter plot would likely have a steeper slope as the general climate on the northern hemisphere is colder.
