A 1-var stat problem with solution.
(1) Find the mean, and standard deviation of the sample:
4.7 17.2 14 6.1 6.1 4.9 9.3 9.4 6.4 6.1
Solution: we have to figure out what and are ourselves (or with the TI-83).
Enter the data into L1: (you can clear L1 now by placing the cursor on L1 on the top of the column and hitting , then moving back down into the list).
After you've done that, you get back to the main screen with . Now you have to run 1-var stats:
and move over right to the Calc Menu:
hit , and then :
Cool, great. Now we're set, we have: n = 10,
A 2 variable stat problem with solution.
(1) The average daily temperature of selected U.S. cities is given, along with the amount of rainfall (in inches) for the month of June:
Daily Temp.| 86 81 83 89 80 74 64
Rainfall | 3.4 1.8 3.5 3.6 3.7 1.5 0.2
(a) Draw a scatter plot, and tell whether the data are negatively or positively correlated
(b) Find the correlation coefficient.
(c) Find the regression line y = ax + b,
(d) Use the regression line to make the specified (in problem) prediction.
Solution:
(1) We're going to do most all of this on the TI-83. So the first thing that we need to do is enter the data. The top row is going to go into the list L1, and the bottom row is going to go into L2. But first, let's make sure things are set up to do statistics. Hit:
, and you are in the stat-plot screen. You want it to look like this:
The 'On' means that the button will plot in statistics mode - scatter plots in this instance since under 'Type:' I have highlighted the first selection, the scatter plot (if you need to, put the cursor on the scatter plot and hit ). Note that 'Xlist' and 'Ylist' are set to L1 and L2, respectively, which means those lists will contain the x's and y's for our regression problems. Finally the 'Mark:' denotes the character that will be displayed when the scatter plot is drawn - the dot at the end is a bad one to choose here.
Head back to the main screen by hitting: . Now let's enter the data into L1 and L2. Hit: to get into the edit menu. Clear out the list L1 - use the direction button to place the cursor on L1: and hit - now use the down direction button to get back into the list, which will clear out all of the entries that were there: . Now do the same thing in the list L2 to clear out it's entries, then move back to L1, enter the data from the top row. Move over to L2, and enter all of the data from the second row:
Now, head back to the main screen: .
(a) Now, we'll draw the scatter-plot. Just hit . you probably won't be able to see anything the first time around, so now re-size the screen automatically by typing: , and you should see the plot: The dots are moving up as we move from left-to-right, so the correlation is positive. It also looks like the correlation is going to be strong. Of course, we'll know for sure here in a second.
(b)-(c) Go back to the main screen: . We're going to run 'LinReg(ax+b)', and place the regression line in the function Y1, so that we can see it along with the scatter plot. Here are the keystrokes:
and right-direction button, to get the CALC sub-menu: Now,
hit for 'LinReg(ax+b)', and you'll be back at the main screen:
Now, one last finesse before we enter- we're going to put the regression line into Y1:
right-direction button to Y-VARS and :
Cool, now hit : As suspected, the correlation coefficient is positive and strong (r = .951....). ( If you don't see the statistic r here, you're going to need to go to the catalog and cut DiagnosticOn: , and use the down direction button on the long list until you see and hit twice. )
The regression line has been placed into Y1: hit : , and you can see the equation there - to graph it, just hit : , and you can see that the data clusters nicely around the regression line.
(d) To use the regression line to predict the rainfall when the temperature is 85, you have to plug x = 80 into the equation of the line. You can do this by hand, or on the TI-83 with for value, and enter the number: : , so the #inches of rainfall would be 3.09 inches.
These are the steps for doing all of these problems.