Line of Best Fit: y=- 0.9328x+77.7 Correlation: Very strong Average Temperature in New Jersey: About 40^(∘)
Practice makes perfect
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 Dataset 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.
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. Note that we will leave out Trenton New Jersey as a data point as we do not know it's average temperature.
Making a Scatter Plot
To make a scatter plot of the data, press 2nd and then Y= and choose plot 1. In plot 1, turn on the scatter plot, choose L1 and L2 as the x- and y-lists as well as an appropriate mark for the data points.
Before pressing GRAPH, we might want to change the Window so it fits our data. To do that we press WINDOW.
Finally, by pressing GRAPH we can plot our values.
Calculate Linear Regression
Once the values are entered, we can perform a linear regression. Press STAT and then use the keypad to choose the CALC menu. Here we have all available types of regressions the calculator can carry out.
By choosing the fourth option, LinReg ax+b, the calculator calculates a linear regression on our data set.
The linear regression is y=- 0.9328x+77.7 and has a correlation coefficient of - 0.9902 which means it fits the data very well. Let's graph this line over the scatter plot.
To estimate the average temperature of Trenton, New Jersey, we substitute the latitude of this city into our line of best fit and calculate the corresponding y-value.
