Suppose (X,Y) follow a joint pdf given by

Suppose (X,Y) follow a joint pdf given by

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1- Suppose (X,Y) follow a joint pdf given by

f(x,y (x+y), 0<x<1.

and zero elsewhere. Find the "Regression function" of Y on x, ie. E(YIX=x), and show that if you take the expectation of this function over x, you get E(Y). Find also Var(YIX=x).

Ht	Wt
169.6	71.2
166.8	58.2
157.1	56.0
181.1	64.5
158.4	53.0
165.6	52.4
166.7	56.8
156.5	49.2
168.1	55.6
165.3	77.8

1.        Draw a scatterplot of Wt on the vertical axis versus Ht on the horizontal axis. On the basis of this plot, does a simple linear regression model make sense for these data? Why or why not?

2.   Show that .7 = 165.52, 7 = 59.47, SXX = 472.076, SYY = 731.961, and SXY = 274.786. Compute estimates of the slope and the intercept for the regression of Y on X. Draw the fitted line on your scatterplot.

Regression through the origin Occasionally, a mean function in which the intercept is known a priori to be zero may be fit. This mean function is given by

E(ylx) = Aix

The residual sum of squares for this model, assuming the errors are independent with common variance a², is RSS =E(yi - filx0²

1. Show that the least squares estimate of /31 is              = xiyi/ Ex?.

Show that /31 is unbiased and that Var(/30 = a²/ Ex?. Find an expression for 6‘². How many df does it have?