3) [30 points] A random sample of 500 owners of single-family homes is drawn from the population of a city. Let the random variable X denote annual household income, in 000 dollars, and the random variable y denote the value of the house, also in 000 dollars. The following information is available: n=500 E (X) = 24,838 E (Y) = 107,226 E (X-X )2 = 66,398 (Y-Y)2 = 1,398,308 E (X- X )(Y-Y ) = 194,293 = a) b) Calculate the mean and standard deviation of X and Y. Compute the correlation between income and house value. Construct a 95% confidence interval for Y. Using a 2-tailed test at the .01 level, test the hypothesis that the correlation between X and Y is zero. Calculate the intercept and slope coefficients from a regression of Y on X What do you suggest are the properties of those estimators you obtained in (e) above given the classical assumptions hold e) 3) [30 points] A random sample of 500 owners of single-family homes is drawn from the population of a city. Let the random variable X denote annual household income, in 000 dollars, and the random variable y denote the value of the house, also in 000 dollars. The following information is available: n=500 E (X) = 24,838 E (Y) = 107,226 E (X-X )2 = 66,398 (Y-Y)2 = 1,398,308 E (X- X )(Y-Y ) = 194,293 = a) b) Calculate the mean and standard deviation of X and Y. Compute the correlation between income and house value. Construct a 95% confidence interval for Y. Using a 2-tailed test at the .01 level, test the hypothesis that the correlation between X and Y is zero. Calculate the intercept and slope coefficients from a regression of Y on X What do you suggest are the properties of those estimators you obtained in (e) above given the classical assumptions hold e)