Question

Create a simulated bivariate data set consisting of n 100 (xi, yi) pairs: Generate n random a-coordinates c from N(0, 1) Generate n random errors, e, from N(0, o), using o 4. Set yiBoB1x; + , Where Bo = 2, B1 = 3, and eN(0, 4). (That is, y is a linear function of , plus some random noise.) (Now we have simulated data. We'll pretend that we don't know the true y-intercept Bo 2, the true slope B 3, the true o= 4, or the true errors e. All we know are the data, (r, Yi). We'll let linear regression estimate the coefficients.) Make a graph of the data and model: Make a scatterplot of the data, (ri, ) Estimate a linear regression model of the form i Bot Bjx Display a summary of the model; check that the estimated coefficients are near the true Bo 2 and B1 3 Add a solid black estimated regression line to the plot. Add a dashed red true line (y 2 3x) to the plot. Add dotted blue 95% pointwise confidence bands that consist, for each prediction (ai,jt), of a vertical confidence interval around y centered at (a,Ý;); the formula is jittn 2,a/28; where is the predicted y at i (this is available in the model you calculated) ei the th residual (this estimate of c is available in the model you calculated) Σ.4 -1 (this is an estimate of o) n-2 () Σ E 3 S tn 2a/2 is the number that cuts off a right-tail area .025 from a Student's t distribution with n - 2 degrees of freedom Add a legend identifying each of the black, red, and blue lines.

R STUDIO

Answer 1

ANSWER R code -for given data :- Genenating d0 andom -Coiatnates X- im fiom No,1) nno n (to0 0,1) im Greneoating eps lon lo0 andom eyyoNS morm(100, 0, 4) e Pai lon plot yim NX. model Im (yN -im) hauns a bline (model col Summary (Im (yx -im) glack)