Find a line of best fit and predict a value

Enter paired data to find the linear regression equation and correlation coefficient, then estimate y for a new x.

6 steps

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Given a set of paired values, you need a straight-line equation and a prediction for a new $x$ . For this example, enter these five pairs:

x y 1224354455

Find the linear regression line $y = a + b x$ , then estimate $y$ when $x = 6$ .

Enter the pairs, fit the line, and predict y

Below each step is the screen you should see after pressing.

Next to each step is the screen you should see after pressing.

Step 1

Open the mode menu and tap Statistics, then choose $y = a + b x$ . The table has an $x$ column and a $y$ column. Start with an empty table; see below if old data is still there.

Press:
Step 2

In the first $x$ cell, enter $1, 2, 3, 4, 5$ , pressing the equals key after each value. The cursor moves down the column; the $y$ cells stay empty until you fill them.

Press:
Step 3

Tap the first $y$ cell. Enter $2, 4, 5, 4, 5$ , pressing the equals key after each value. The empty $y$ cell in row 6 is selected when you finish.

Press:
Step 4

Press the equals key on that empty cell, then tap Reg Results. Read the $y = a + b x$ block: $a = 2.2$ , $b = 0.6$ , and $r = 0.7745966692$ . Check that it is marked In use.

Press:
Step 5

Tap the arrow at the top-left of the results list to return to the table. Press the equals key on the empty row, then tap Statistics Calc. Its header should show $y = a + b x$ .

Press:
Step 6

Enter $6$ , then open Statistics variables with the keys shown. It opens at Regression; tap $\overset{y}{^}$ . Press the equals key: the input is $6 \overset{y}{^}$ and the answer is $5.8$ .

Press:

Read and check the result

In $y = a + b x$ , $a$ is the intercept and $b$ is the slope. The fitted line is:

y = 2.2 + 0.6 x

The same block shows the correlation coefficient $r = 0.7745966692$ . Check the prediction by substituting $x = 6$ :

\overset{y}{^} = 2.2 + 0.6 \times 6 = 5.8

Here $\overset{y}{^}$ means the estimated $y$ for the $x$ typed before it. Enter it after the number: $6 \overset{y}{^}$ .

The line of best fit is the straight line $y = a + b x$ , so keep it marked In use: that is the fit the prediction uses. The other six blocks are curves; Reg Results lists them for comparison and does not choose one for you.

Other ways to estimate y

Under the seven blocks of Reg Results, the Estimate buttons open Statistics Calc with that estimate already typed after an empty box: tap $\overset{y}{^}$ , enter $6$ in the box and press the equals key to get $5.8$ .

If your result is different

Old numbers are still in the table: tap the trash button on the function bar under the screen, then confirm with Delete All. This removes the old data before you enter the example.
A $y$ cell is still empty: enter every $y$ value. A row without a $y$ is left out of the fit, so the line changes.
The wrong fit is selected: return to Reg Results and tap the $y = a + b x$ block. Check the fit named in the Statistics Calc header before predicting.
The results list covers the keys: use its top-left arrow to return to the table.
A cell shows Syntax ERROR: press AC to clear the error.

The fx-991EX Statistics Calc screen showing 6ŷ with the predicted value 5.8.

Find a line of best fit on your fx-991EX calculator

Enter the five pairs, find y = 2.2 + 0.6x, and use the line to predict y when x = 6.

Fit the line More guides

Enter the pairs, fit the line, and predict y

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Read and check the result

Other ways to estimate y

If your result is different

Find a line of best fit on your fx-991EX calculator