Question

I need to find the weighted least square line (y = ß0 + ß1X ) for a set of 5 data sets, but I have to suppose that the first and last pair are less reliable and therefore should only have half the weight than the rest of the 3 pairs.

This are the pairs (-2, 0), (-1, 0), (0, 2), (1, 4), (2, 4)

I already saw tutorial on how to calculate ordinary least squares. But I don´t know how to assign just half the weight to the first and last pair and reflect that on Excel. Is there a formula or how do I give them less weight?

Thanks for your help

Answer 1

You need to find the variance and divide the data by variance. Once it is done then you can go ahead and use ordinary least squares.

Weighted X-X/Variance 0.8 Weighted Y-X/Variance Weighted Y= X/Variance 0.5 Y-0.75x+0.5 0.8 Varinace SUMMARY OUTPUT Regression Statistics MultipleR RSquare Adjusted RSquare Standard Error Observations 0.948683298 0.9 0.182574186 06-042 0.2 0,4 0.6 ANOVA MS incance F Regression Residual 0.9 0.1 0.03333 0.9 27 0.01385 Coefficients ndard Err tStat P-value ower 95pper 95%bwer 95.0 Opper 95.0% Intercept X Variable 1 0.5 0.08165 6.12372 0.00875 0.24015 0.75985 0.24015 0.75985 0.75 0.14434 5.19615 0.01385 0.29065 1.20935 0.29065 1.20935