(1) A researcher is using data for a sample of 1000 houses sold in an urban area during a recent year to investigate the relationship between house prices yi (measured in thousands of dollars) and house size xi (measured in square meters). Preliminary analysis of the sample data produces the following sample information: N=1,000,i=1nyi=25,835,i=1nxi=16,462i=1nyi2=8,500,750,i=1nxi2=3,329,789,i=1nxiyi=5,209,990i=1n(xix)(yiy)=377,534,i=1n(yiy)2=917,854i=1n(xix)2=250,144,i=1nu^i2=348,053 Use the above sample information to answer the following questions: a) Compute OLS estimates of the intercept and slope coefficients in the simple linear regression model. Interpret the estimates. (4p) b) Calculate an estimate of 2; the residual variance. (4p) c) Compute the value of R2, the coefficient of determination for the estimated OLS sample regression equation. Briefly explain what the estimated value of R2 means. (4p) d) Compute a 95% confidence interval for the slope coefficient 2 : Interpret the result. (4p) e) Perform a test of the null hypothesis H0:2=1 against the alternative hypothesis H1:2=1 at the 5% significance level. Briefly explain what the test outcome means. (4p)