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Does this plot indicate that age is a reasonable choice of regressor variable in this model 11-13. Show that in a simple linear regression model the point ( x, y ) lies exactly on the least squares regression line. 11-14. Consider the simple linear regression model Y 0 . Suppose that the analyst wants to use z x x as the 1x regressor variable. (a) Using the data in Exercise 11-12, construct one scatter plot of the ( xi, yi) points and then another of the ( zi xi x, yi ) points. Use the two plots to intuitively explain how the two models, Y and 0 1x * *z , are related. Y 0 1 (b) Find the least squares estimates of * and * in the model 0 1 * *z . How do they relate to the least Y 0 1 squares estimates 0 and 1 Linear Barcode generation in .netgenerate, create 1d none with .net projects* 11-15. Suppose we wish to t the model y* i 0 * 1xi x 2 , where y* yi y (i 1, 2, p , n). Find 1 i i the least squares estimates of * and *. How do they relate 0 1 to 0 and 1 11-16. Suppose we wish to t a regression model for which the true regression line passes through the point (0, 0). The appropriate model is Y x . Assume that we have n pairs of data (x1, y1), (x2, y2), p , (xn, yn). Find the least squares estimate of . 11-17. Using the results of Exercise 11-16, t the model Y x to the chloride concentration-roadway area data in Exercise 11-11. Plot the tted model on a scatter diagram of the data and comment on the appropriateness of the model.Print qr code iso/iec18004 for .netusing .net framework crystal topaint qrcode on asp.net web,windows application11-3Barcode encoder with .netuse .net bar code integration toreceive barcode for .netPROPERTIES OF THE LEAST SQUARES ESTIMATORS 2D Barcode writer on .netusing barcode printer for visual .net crystal control to generate, create 2d matrix barcode image in visual .net crystal applications.The statistical properties of the least squares estimators 0 and 1 may be easily described. Recall that we have assumed that the error term in the model Y is a random 0 1x variable with mean zero and variance 2. Since the values of x are xed, Y is a random vari2 able with mean Y 0 x . Therefore, the values of 0 and 1 depend 0 1x and variance on the observed y s; thus, the least squares estimators of the regression coef cients may be viewed as random variables. We will investigate the bias and variance properties of the least squares estimators 0 and 1. Consider rst 1. Because 1 is a linear combination of the observations Yi, we can use properties of expectation to show that expected value of 1 is E1 1 2I Interleave Barcode barcode library on .netusing barcode development for visual .net control to generate, create i2 of 5 barcode image in visual .net applications.(11-15)DataMatrix implementation on .netusing barcode drawer for asp.net web forms control to generate, create 2d data matrix barcode image in asp.net web forms applications.Thus, 1 is an unbiased estimator of the true slope EAN-13 Supplement 5 barcode library for .netUsing Barcode decoder for visual .net Control to read, scan read, scan image in visual .net applications.CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION Barcode Pdf417 scanner for noneUsing Barcode Control SDK for None Control to generate, create, read, scan barcode image in None applications.Now consider the variance of 1. Since we have assumed that V( i) 2 , and it can be shown that V(Yi) V1 1 2 For the intercept, we can show that E1 0 2 and V1 0 2Control european article number 13 size with .net european article number 13 size for .net, it follows that scan ecc200 in .netUsing Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.(11-16)Control ean-13 supplement 5 size in visual c#to incoporate gtin - 13 and ean13+2 data, size, image with c# barcode sdk1 cn Render barcode standards 128 for .netusing rdlc report toprint barcode 128 with asp.net web,windows applicationx2 d Sxx Develop gs1 datamatrix barcode with excelusing barcode drawer for office excel control to generate, create data matrix barcodes image in office excel applications.(11-17)Thus, 0 is an unbiased estimator of the intercept 0. The covariance of the random variables 2 and is not zero. It can be shown (see Exercise 11-69) that cov( , ) x Sxx. 0 1 0 1 2 The estimate of could be used in Equations 11-16 and 11-17 to provide estimates of the variance of the slope and the intercept. We call the square roots of the resulting variance estimators the estimated standard errors of the slope and intercept, respectively. De nition In simple linear regression the estimated standard error of the slope and the estimated standard error of the intercept are se1 1 2 B Sxx