Calculate linear regression (1,2)(2,4)(3,5)(4,4)(5,5)

Linear regression, confidence intervals, expected value, and covariance.

Data

Answer

y = 0.6x + 2.2 (R²=0.6)

To find the line of best fit for 5 data points using least squares regression, we need the slope (m) and y-intercept (b) of y = mx + b.

Step 1 — List the data points

(1, 2), (2, 4), (3, 5), (4, 4), (5, 5)

Step 2 — Compute the required sums

n = 5

Σx = 15, Σy = 20

Σxy = 66, Σx² = 55

Step 3 — Calculate the slope (m)

Using the least squares formula:

m = (nΣxy − ΣxΣy) / (nΣx² − (Σx)²)

= (5 × 66 − 15 × 20) / (5 × 55 − 15²)

= 30 / 50

m = 0.6

Step 4 — Calculate the y-intercept (b)

b = (Σy − mΣx) / n

= (20 − 0.6 × 15) / 5

b = 2.2

Step 5 — Measure the fit

The correlation coefficient r = 0.7746 measures how closely the data follows a linear pattern.

R² = 0.6

This means 60% of the variation in y is explained by x.

Interpretation: moderate positive correlation.

y = 0.6x + 2.2 (R² = 0.6)

To compute linear regression (1,2)(2,4)(3,5)(4,4)(5,5), apply the statistical formula to the data points.

This is a statistical analysis — advanced statistics includes regression, hypothesis testing, and measures of association.

What is the answer to linear regression (1,2)(2,4)(3,5)(4,4)(5,5)?
The answer is y = 0.6x + 2.2 (R²=0.6).

What method is used?
Linear regression finds y = mx + b that best fits the data. R² measures how well the line fits.

More advanced statistics calculator problems