Consider the data from 6.1 from our textbook.

x = Age

y = Income

From Excel and MATLAB, b₀ = 6.390598 and b₁ = 1.494302.

Use R to compute for the slope and intercept

Simple Regression American Express Study ... Age Income 0.7032 Coefficient of Determination X Y Error Confidence Interval for Slope 0.8386 Coefficient of Correlation 69 113 3.502564 1-a (1-a) C.I. for By 52 91 6.905698 95% 1.494302 + or - 0.791534 s(b ,) 0.343249 Standard Error of Slope 65 121 17.47977 58 81 -12.0601 Confidence Interval for Intercept 5 31 68 15.28604 1-a (1-a) C.I. for Bo 6 51 92 9.4 95% 6.390598 + or - 41.44344 s(bo) 17.97197 Standard Error of Intercept 53 75 -10.5886 56 76 -14.0715 Prediction Interval for Y 42 56 -13.1513 1-a X (1-a) P.I. for Y given X 10 33 53 -2.70256 + or - S 12.86154 Standard Error of prediction Prediction Interval for E[Y X] 1-a X (1-a) P.I. for E[Y [ X] + or - ANOVA Table Source SS df MS F F critical p-value Regn. 3135.046 1 3135.046 18.95211 5.317655 0.0024 Error 1323.354 8 165.4193 Total 4458.4New to MATLAB? See resources for Getting Started. X >> x=[69 52 65 58 31 51 53 56 42 33] ; >> y= [113 91 121 81 68 92 75 76 56 53]; >> mdl=fitlm(x, y) mdl = Linear regression model: y ~ 1 + x1 Estimated Coefficients: Estimate SE tStat pValue (Intercept) 6. 3906 17.972 0. 35559 0. 73134 x1 1. 4943 0. 34325 4.3534 0. 0024341 Number of observations: 10, Error degrees of freedom: 8 Root Mean Squared Error: 12.9 R-squared: 0.703, Adjusted R-Squared: 0.666 F-statistic vs. constant model: 19, p-value = 0. 00243