Suppose we observe independent and identically distributed (Wi, Yi) and we solve the least squares problem = argminb n1 !n i=1{Yi mb(Wi)}2 to fit the two models mb(w) = b0 +b1w and mb(w) = b0 +b1w +b2w2. The data is shown in the plot below.

> model=lm(Y~1+W) > model Call: lm(formula = Y ~ 1 + W) Coefficients: (Intercept) W 0.4681 0.2773 > vcovHC(model) (Intercept) W (Intercept) 0.0003177102 -0.0003076706 W -0.0003076706 0.0003713042 > > model=lm(Y~1+W+I(W^2)) > model Call: lm(formula = Y ~ 1 + W + I(W^2)) Coefficients: (Intercept) W I(W^2) -0.05722 2.09151 -1.05576 > vcovHC(model) (Intercept) W I(W^2) (Intercept) 0.0001092720 -0.0002563260 0.0001252932 W -0.0002563260 0.0007651937 -0.0004146568 I(W^2) 0.0001252932 -0.0004146568 0.0002388900 > 4. Suppose that our modeling error t(m)t(m) is ten times larger with the less accurate model than with the more accurate one. Using your work from the previous part, determine whether confidence intervals based on the less accurate model will contain t(m) much more frequently, much less frequently, or about equally frequently. What if, instead, modeling error were two times larger but the variance of the estimators remained the same? Or 1.5 times larger? Explain your answers

C:/Users/user/Downloads/davincy.pdf - + D A DV 12 0.8 0.4- 00 00 1.0 15 w 1 Sketch the dati plotted nove atid, on top of it sketch both model s. timates mut)Draw the first with a solid line and the second with a dashed lite. These sketches do not need to be accurate, but the whold lenswer the following question 2. Sit were estimating m - m - For which model will the time be more accurate? Westimate tused on the cher model be too large or too small Explain why 2. For both models, procedente interviewed on the followim Shwarter work. Pe stron intervals in the form is with the deciples No need to be all that presenti in The following powerful @ C:/Users/user/Downloads/davincy.pdf - + D A DV 12 0.8 0.4- 00 00 1.0 15 w 1 Sketch the dati plotted nove atid, on top of it sketch both model s. timates mut)Draw the first with a solid line and the second with a dashed lite. These sketches do not need to be accurate, but the whold lenswer the following question 2. Sit were estimating m - m - For which model will the time be more accurate? Westimate tused on the cher model be too large or too small Explain why 2. For both models, procedente interviewed on the followim Shwarter work. Pe stron intervals in the form is with the deciples No need to be all that presenti in The following powerful @