c Is a linear regression really the best fit if you look at the curve?
D
d Would a new linear regression including the new data point come closer or further away from the new data point?
A
aScatter Plot:
Line of Best Fit: y=4.82x-29.65 Scatter Plot and Line of Best Fit:
B
b About 404 feet
C
c See solution.
D
dSlope: Steeper
y-intercept: Lower
Practice makes perfect
a Our objective is to make a scatter plot of the given data, find the line of best fit, and finally to graph the line of best fit on top of our scatter plot.
Car Stopping Distance
Speed (mi/h)
10
15
20
25
30
35
40
45
Stopping Distance (ft)
27
44
63
85
109
136
164
196
We will start with making a scatter plot.
Make a Scatter Plot
To make a scatter plot from the data we first have to enter the values into lists. Push STAT, choose the EDIT menu, and then press ENTER on the first option, Edit. We can enter the values in the first two columns.
Having entered the values, we can plot them in a scatter plot by pushing 2nd and Y=. Then, we will choose one of the plots in the list. Make sure you turn the plot ON, choose the type to be a scatter plot, and assign L1 and L2 as XList and Ylist. Finally, you can pick whatever ever type of mark you want.
Now you can draw the plot by pressing GRAPH. However, the standard viewing window is not going to show all data points. Therefore, we first have to press WINDOW and change the window settings to something that will fit the data points.
Line of Best Fit
To find the equation of the line of best fit, we have to perform a linear regression on our data points. To do this we press the button STAT and then choose the CALC menu. The regression we want to perform is under the fourth option, LinReg(ax+b). By pressing ENTER the calculator performs a linear regression.
The linear regression gives us y=4.82x-29.65.
Draw Line of Best Fit
Having rewritten the equation, we can enter it in our calculator by pressing Y=. When the equation has been entered in the calculator, plot it by pressing GRAPH.
b To predict the stopping distance at 90 mihr, we substitute x=90 in the line of best fit and evaluate.
The stopping distance at 90 mihr is about 404 feet.
c If we look at the scatter plot, we see that it shows a slight curve upwards.
This means a linear regression might not be the best fit for the data points when reaching higher speeds. The stopping distance at 90 mihr was predicted using the line of best fit. However, had we had used an exponential model the prediction would likely be more accurate.
d We are given a new data point. First, let's change the window so that it fits this point as well. By pressing GRAPH, we see our settings with these new window settings.
If we would include the new data point when performing the linear equation, the equation would be steeper and have a lower y-intercept to adjust to the data.
