#### Exploring Data: Linear Models and Scatter Plots

Exploring Data: Linear Models and Scatter Plots

TI83 Users Only:

There is a correlation coefficient that is mentioned in many books. By default, the TI83 doesn’t give this to you. You can enable it (you just need to do this once, and then it is done forever much until you lose power or reset your calculator) by going [Catalog] (2nd zero). Then, scroll down to DiagnosticOn (hit D [calculator is already in the alpha mode, thus just hit the inverse key] to get close fast) and press enter twice till the calculator states done.

Correlation and Regression:

The Linear Correlation Coefficient (r) is the measure of strength and direction of a relationship among two variables. If y gets bigger when the x gets bigger, then the coefficient is positive and when y gets smaller when the x gets bigger, the coefficient is negative. If there is no linear relationship between the two variables, then the coefficient is equal to zero. When all the data precisely lies on a line, then it is termed as a perfect correlation and the value will either be 1 or -1. The nearer the value is to 1 or -1, the nearer the points are to the line and the stronger the linear relationship. The similar concept applies for other kinds of regression (that is, the TI82, TI83 and TI85 will do logarithmic, linear, exponential, power, quadratic, cubic and quartic regression).
The Regression Line or Regression Equation is the equation of line which best fits the data.

One of the utilizations of regression is to see if there is a correlation among the two variables. This is pointed out by the value of correlation coefficient r. The other use of regression is to predict the values.

Clearing Existing Data in the Calculator:

TI82/TI83:

It is assume that you are putting the x-coordinates to List 1 and the y-coordinates to List 2. Make suitable modifications to the instructions when you use various lists.

a) Press the [Stat] key.
b) Select the Edit option.
c) Arrow the way to the top (that is, above the line) of the list that you are going to utilize. Generally this will be L1.
d) Hit the [Clear] key.
e) Press the [Enter].
f) Arrow the next list to clear out and repeat the steps c-e.

TI85:

With TI85, you enter pairs of x-coordinates or y-coordinates. When you have just cleared out your data, skip the steps a via c and start on step d.

a) Press the [Stat] key.
b) Select Edit [F2]
c) [Enter] twice to admit the lists xStat and yStat (you can modify names if you wish to).
d) Enter the x-coordinate of first point and press [Enter].
e) Hit the y-coordinate of second point and press [Enter].
f) Repeat the steps d and e for each and every additional point
g) [Exit] twice to get back to main screen.

Scatter Plots:

TI82/TI83:

a) Turn off the entire regular y= plots by going to [y=] and clearing them out (or move to equivalent sign and press enter).

b) Press [StatPlot] (2nd y=).

c) Select Plot1. You can employ any of the three, however for simplicity sake, you can use plot 1.

d) Turn it ON.

e) Select the Scatter Plot (first plot type-with a bunch of dots).

f) For Xlist, select List 1 (L1). On TI82, simply press enter. On TI83, you will require to really put in List 1 by pressing the [2nd] and .

g) For Ylist, select List 2 (L2).

h) The Mark can be whatever thing. It is recommend the little square as it shows up better than the dot or cross.

i) Press [Zoom].

j) Select the Statistics option. Option (i) (simply hitting (i) is faster than scrolling down).

TI85:

On TI85, you should set up the viewing window prior to viewing the scatter plot. As well the ZoomFit option doesn’t work to automatically set the window for data. Though, TI85 does give a simpler way to graph the regression equation.

a) Turn off the entire regular y= plots by going [Graph], y(x) [F1] and either deleting or clearing the functions. You might as well select to leave the graphs however turn them off by empoying [More] and All- [F2]

b) Set your viewing window by selecting Range [F2].

c) Set the values and hence all the data values are exhibited.

d) Press [Stat].

e) Select Draw [F3].

f) Select Scatter Plot [F2].
This will be tough to see the dots on the scatter plot as they are just individual pixels, not boxes or crosses similar to with TI82 or TI83.

Least Squares Regression Line:

The least squares regression model is a line that minimizes the variation. If you really wish to know, then take a statistics class. In general terms this is the line which best fits the data. That is, why it is sometimes termed as the best fit line.

TI82/TI83:

When you have a TI83, make sure that you enable Diagnostics as described at the top of this section. You require to only do that once.

The TI82 and TI83 return regression equation y = ax+b. If you wish the regression equation y = a+bx, then you must select LinReg(a+bx) rather.

a) Press the [Stat] key.

b) Arrow right to Calc screen.

c) Select the ‘LinReg (ax+b)’ option. It is #5 on TI82 and #4 on TI83.

d) State the calculator where you place the data. Enter L1, L2 and hence the screen states ‘LinReg(ax+b) L1,L2’. To enter the L1, press [2nd] . Be sure that you get the comma between L1 & L2. The comma is right above 7.

e) Press [Enter] to run the command.

f) The calculator will return the values for a, b and r (and r^2 on TI83). Write the equation of the regression line as y = ax + b, however actually write the values for a and b.

TI85:

Note: TI85 returns the regression equation y = a+bx. The book and other TI calculators will be employing y = ax+b rather. Be sure to adjust suitably.

If you just plotted your scatter plot, then skip to the step 2.

a) Press [Stat].

b) Select Calc [F1].

c) Press [Enter] twice to admit the lists having your data.

d) Select Linear Regression [F2].

e) The calculator will return y-intercept (a), slope (b) and the correlation coefficient r (corr). The TI85 too returns the number of values (n).

Drawing the Regression Line on the Scatter Plot:

TI82/TI83:

You should calculate the regression equation before doing this.

a) Press [y=]

b) You could re-enter the equation which you wrote down, earlier, however it is a pain to do, and you are likely to lose some correctness whenever you do that. As still waiting to enter the equation to plot, press the [Vars] key.

c) Select Statistics (5).

d) Arrow right to the EQ

e) Select RegEQ. This is the option 7 for TI82 and option 1 for TI83.

f) Press [Graph].

TI85:

You should calculate the regression equation before doing this. When you just calculated the regression equation, skip to the step 2.

a) Press [Stat].
b) Select Draw [F3].
c) Select Draw Regression Equation (DDREG) [F4].

Predicting Values:

One of the utilizations of the regression equation is to predict the values.

TI82/TI83:

You should have calculated the regression equation and place it to y1 to utilize this.

a) Press [TblSet] (2nd Window)

b) The simplest way is to set TblMin to be the value of x you want to predict y for.

c) Set the delta-Tbl to be 1.

d) Press [Table] (2nd Graph).

e) You can scroll via and see other values if you want.

If you wish to find out the value of x which gives a particular y-value, then you require solving the regression equation for x and then replacing the known value of y.

TI85:

You should have calculated the regression equation; however you don’t have to graph it to utilize this. If you have just done the Linear Regression, then skip to the step 2.

a) Press [Stat].
b) Select Forecast (FCST) [F4]
c) Enter the value for x you want to utilize and hit [Enter].
d) With cursor sitting on the y= line, hit Solve [F5].

The TI85 can be utilized to find out the values of x which give a specific value of y. To do that, enter the value for y, place the cursor on x= line and press solve.

When you are all done:

Be sure to turn off the statistical plots and clear out the regression equation whenever you are done.

TI82/TI83:

a) Press [StatPlot] (2nd y=)
b) Select PlotsOff (4)
c) Hit [Enter]

TI85:

You do not have to do something special. The statistical plots and y= plots are kept take apart from one other. If you wish to, though, you might clear your drawing.

a) Press [Graph], [More].

b) Select Draw [F2].

c) Press [More] ClrDrw [F5].

Alternatively, and most likely faster....

a) Press [Stat]

b) Select Draw [F3]

c) Select ClrDrw [F5]

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