Question 2~ With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied)

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Question 2~ With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. A sample of the data is provided below. ~ dollars satisfaction 17~ 10~ 12< 30 10< a) Find the equation of the fitted regression line. ~ b) Estimate the standard deviation of the error term & c) Calculate a 90% confidence interval for B, d) Test the null hypothesis that , = 0 (perform a two-sided test), using a = 0.1. Is the model useful?~ e) Perform the regression using R, and give the p-value to the test in part d). Verify that the p-value agrees with your conclusion in part d).~

Question 1 Suppose we wanted to predict the selling price of a house using its size in a certain area of a city. A random sample of six houses were selected from the area. The data is presented in the following table with size given in hundreds of square feet, and sale price in thousands of dollars. Size (X/) 10 13 16 19 22 25 Price ( )7) 70 95 85 125 130 120 O

3. Consider a bivariate normal population with ( = 0, /2 = 2,011 = 2, 022 = 1, p12 = 0.5. (a) (2 marks) Write out the bivariate normal density. (b) (3 marks) Write out the squared Mahalanobis distance (x - )"E (x - /) as a function of r] and 12. (c) (5 marks) Determine and sketch the constant -density contour that contains 50% of the probability.