Dawnbridge

TI-Nspire CX II field manual for IB Math

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23

Linear regression and r

All courses

Enter paired data into two table columns, enable the calculator's correlation diagnostics, run linear regression, and read the regression equation and r.

Goal

Find the least-squares regression line and correlation coefficient for ​(1,2.1),  ​(2,2.9),  ​(3,3.7),  ​(4,4.6),  ​(5,5.1).

1

Open a Lists & Spreadsheet page, name the first column x, and enter 1, 2, 3, 4, 5. Name the second column y, and enter 2.1, 2.9, 3.7, 4.6, 5.1.

*Document
RAD
AxByCD=112.1222.9333.7444.6555.1A1
2

Run linear regression: press → 4: Statistics → 1: Stat Calculations → 3: Linear Regression (mx+b). Set X List = x and Y List = y, moving between fields with .

*Document
RAD
AxByCD=112.1222.9333.7444.6555.1A1
Linear Regression (mx+b)
X List:x[]▶
Y List:y[]▶
Frequency List:1▶
Category List:▶
1st Result Column:c[]▶
OKCancel
3

Set 1st Result Column to an empty column, such as c[], so the Nspire writes the regression equation, ​r, and ​r2​ into the spreadsheet. Press to calculate.

*Document
RAD
ByCDE==LinRegMx12.1TitleLinear R...22.9RegEqnm*x+b33.7m0.7744.6b1.3755.1r²0.993465B1
Result

The regression line is ​y≈1.37+0.77x, and the correlation coefficient is ​r≈0.997.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find the regression line and ​r​ for ​(1,3.8),  ​(2,5.1),  ​(3,6.4),  ​(4,8.2),  ​(5,9.3),  ​(6,10.9).

  2. 2

    Find the regression line and ​r​ for ​(1,9.2),  ​(2,7.9),  ​(3,6.1),  ​(4,4.8),  ​(5,3.5).

  3. 3

    Find the regression line and ​r​ for ​(2,3.1),  ​(4,4.9),  ​(6,7.2),  ​(8,8.8),  ​(10,11.3).