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A residual is our observed value minus. What wed expect our predicted value so so from the day 22 problem the tree that was 14 feet tall had an yield of 974 now using our equation from that problem we can calculate what wed expect the yield for a 14 foot tree to be so our predicted yield is 21 point three nine times fourteen feet plus 231 point nine. One so our predicted yield is 531 point for approximately.

So our residual is 442 point. Six three pounds. Now a positive residual means.

This tree had a higher yield than wed expect so we can say the 14 foot tree had an avocado yield of 442 point six three pounds over what our model would predict were going to use our calculator to help us make the residual plot. If we press stat and then edit. We already input all of the avocado tree heights in list one and all the yields in list two then if you press stat and calculate and go down to linear regression.

We can calculate our model so theres our slope and y intercept now were going to calculate a residual plot so to do this press the stat button and then enter on edit now in list one is all of our tree heights and enlist two is the yields we saw for each of those tree heights. These are the actual observed values so enlist three we want the expected values so for each tree height in list one what would our equation. Predict the yield would be thats what we want in list three so to do this press up.

Now list three is highlighted and this is our function bar down here. So if you press vars and you go down to statistics. And you go over to equation.

The first option is reg equation. Our regression equation.

So when we press enter. There it actually pasted our regression equation right down in the function bar. Now the only thing we need to do is see where this xs we need to replace that with list one so well highlight x.

And press second one and what thats going to do is take each of our tree heights and list one multiply it by our slope and then add our y intercept. So when i press enter heres all of our predicted values or our expected values now. Were ready to calculate the residuals.

A residual is the observed value minus the expected value so our observed values are in list two and im gonna subtract the expected values in list three so to type any list just press second and then the list number. So i did second two minus sign and then second three for this command now im gonna press enter all right theres all of our residuals now a negative residual means we observed less than what our model would predict where a positive residual means. We had a higher yield than what our model would predict for that tree height.

Now lets make the residual plot. Im going to press second and y equals to get to the stat plot menu and im going to press enter on plot one on a residual plot. The x axis is going to be our explanatory variable so in this case.

Its tree height. So well leave list 1. There our vertical axis is going to be the residual so im gonna change this to list.

4. Which is where our residuals are stored.

Now if i press zoom and then the number 9 heres my residual plot. And you may notice. Its actually very similar to the original scatterplot just rotated.

So that the model line is horizontal. Now if we have to copy this down. Were gonna need some of these values.

So theres a trick. If you press this trace button right here as you scroll through it will show you the x and y coordinates of these different. Points.

The only bummer is it does it in list order right now so it kind of jumps from point to point all over the place. But it will give you some idea of what scale to use when you copy down this residual plot. But since we have the plot on our calculator screen.

Were going to jump right to describing it so for our description. Im gonna say the residual plot shows random scatter through the various tree heights. When we look at the residual plot.

The scatter seems random and the x axis is our tree heights. And i dont see the residuals either increasing or decreasing as tree height increases or decreases.

So its a random scatter thats a good sign. Another good sign is most our residuals seem fairly small with the exception of these two right here. Most the residuals are pretty close to the line that means our model gets fairly close to predicting the actual yield.

I am going to talk about these two values these are from trees of heights 14 and 16 and since theyre large positive residuals it means our model under predicted their yield substantially but overall a linear model seems quite appropriate now the formula for calculating r squared and s is pretty complicated. But we already have the data stored in the calculator. So heres what were gonna do first press mode.

And hopefully your calculator has this if you go down. Theres something called stat diagnostic. And you want to turn that on now press 2nd quit to get out of that screen and push the stat button go to calculate and were going to rerun our linear regression option for here now we see some extra output.

We have our which is our correlation in our squared. So well write down our squared and r squared has a really neat interpretation as you look at the original scatterplot you can see that the yield varied. Quite a bit.

Theres a lot of variation in yield. Well how much of that variation what percent of that variation can be explained by the tree. Height thats what our squared.

Measures so well say about 40 175. Percent of the variation in yield can be explained by tree height to calculate s press.

Stat and go over to the test menu. Now option f. On my calculator.

Is linreg t test. If you click that and for x list. You use list 1 and y list list to ignore everything else.

And just press calculate now right here at the bottom. This is our s value. And youre actually going to learn what all these other things are later in your statistics course.

But right now lets just focus on that s value now s. Is actually a standard deviation of the residuals and to interpret it well say the average error when predicting yield from tree height using our least squares regression equation is about one hundred and fifty five point three zero two pounds r squared measures the strength of the relationship between two variables so changing the units would not affect its value s. However is measured in the same units.

As the response variable and changing units in either. The explanatory or the response variable would cause its value to change. If you liked this video and want to learn more about scatter plots least squares.

Regression residuals and how to use your calculator check out this playlist. Lots of students have found the first video on the playlist particularly helpful. .

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