INTERPRETATION OF THE SLOPE: The slope of the best-fit line tells us how the dependent variable ( y ) changes for every one unit increase in the independent ( x ) variable, on average.
Third exam vs final exam example
Slope: The slope of the line is b = 4.83.Interpretation: For a one-point increase in the score on the third exam, the final exam score increases by 4.83 points, on average.
Using the Linear Regression T Test: LinRegTTest
- In the STAT list editor, enter the X data in list L1 and the Y data in list L2, paired so that the corresponding ( x , y ) values are next to each other in the lists. (If a particular pair of values is repeated, enter it as many times as it appears in the data.)
- On the STAT TESTS menu, scroll down with the cursor to select the LinRegTTest. (Be careful to select LinRegTTest, as some calculators may also have a different item called LinRegTInt.)
- On the LinRegTTest input screen enter: Xlist: L1 ; Ylist: L2 ; Freq: 1
- On the next line, at the prompt β or ρ , highlight "≠ 0" and press ENTER
- Leave the line for "RegEq:" blank
- Highlight Calculate and press ENTER.
The output screen contains a lot of information. For now we will focus on a few items from the output, and will return later to the other items.
The second line says
y =
a +
bx . Scroll down to find the values
a = –173.513, and
b = 4.8273; the equation of the best fit line is
ŷ = –173.51 + 4.83
x
The two items at the bottom are
r
2 = 0.43969 and
r = 0.663. For now, just note where to find these values; we will discuss them in the next two sections.
Graphing the Scatterplot and Regression Line
- We are assuming your X data is already entered in list L1 and your Y data is in list L2
- Press 2nd STATPLOT ENTER to use Plot 1
- On the input screen for PLOT 1, highlight On , and press ENTER
- For TYPE: highlight the very first icon which is the scatterplot and press ENTER
- Indicate Xlist: L1 and Ylist: L2
- For Mark: it does not matter which symbol you highlight.
- Press the ZOOM key and then the number 9 (for menu item "ZoomStat") ; the calculator will fit the window to the data
- To graph the best-fit line, press the "Y=" key and type the equation –173.5 + 4.83X into equation Y1. (The X key is immediately left of the STAT key). Press ZOOM 9 again to graph it.
- Optional: If you want to change the viewing window, press the WINDOW key. Enter your desired window using Xmin, Xmax, Ymin, Ymax
Note
Another way to graph the line after you create a scatter plot is to use LinRegTTest.
- Make sure you have done the scatter plot. Check it on your screen.
- Go to LinRegTTest and enter the lists.
- At RegEq: press VARS and arrow over to Y-VARS. Press 1 for 1:Function. Press 1 for 1:Y1. Then arrow down to Calculate and do the calculation for the line of best fit.
- Press Y = (you will see the regression equation).
- Press GRAPH. The line will be drawn."
The correlation coefficient r
Besides looking at the scatter plot and seeing that a line seems reasonable, how can you tell if the line is a good predictor? Use the correlation coefficient as another indicator (besides the scatterplot) of the strength of the relationship between x and y .