Exam 11: Regression Analysis I

Suppose that n = 21, $\bar{x}$ = 38.044, $\bar{y}$ = 89.27, S_xx = 994.045, S_xy = 6191.08, and S_yy = 76,293.5. A) Obtain the equation of the best fitting straight line. B) Calculate the residual sum of squares. C) Estimate . Round your answers to three decimal places.

Consider the following data. A) Calculate the least squares estimate . B) Calculate the least squares estimate . C) Estimate the error variance . D) Test H₀: $\beta$ ₁ = 0 versus H₁: $\beta$ ₁ $\neq$ 0 with $\alpha$ = 0.05. Answer "H₀ is rejected at $\alpha$ = 0.05" or "H₀ is not rejected at $\alpha$ = 0.05". E) Estimate the expected y value corresponding to x = 3. F) Give a 90% confidence interval for the expected y value at x = 3. Round your answer to two decimal places.

An internet site lists the prices, y, of a used popular midsized model foreign car. The age, x, in years and the price(thousands $) are given in the table for a sample of six cars. (a) Determine the least squares regression line. (b) Estimate the price of a used car of this model whose age is 9. (c) Give a 95% prediction interval for the price of a used car of age 9. (d) Besides the uncertainty accounted for in the calculation in Part c, what else could lead to a serious mistake in the pre- diction.

One measure of the development of a country is the Human Development Index (H.D.I.) which combines life expectancy, literacy, and gross domestic product per capita into an index whose values lie between 0 and 1, inclusive. We randomly selected 12 countries, of the 182 countries on the list. H.D.I. is the response variable y, and total fertility rate (births per woman), x, is the predictor variable. The data have the summary statistics. n = 12 $\bar{x}$ = 1.825 $\bar{y}$ = .85 S_xx = 2.7625 S_yy = .0342 S_xy = -.1838 A) Estimate the mean value of H.D.I. for the total fertility rate of 2.5. B) Construct a 95% confidence interval for the response in part A. Round your answer to three decimal places.

Calculate the correlation coefficient between the number of grocery carts, x, ahead in line and the time, y, to complete checkout.

An advertising company collected data on the number of new contracts signed, y, and the number of presentations, x, made in each of six months. The summary statistics are n = 6 $\bar{x}$ = 34 $\bar{y}$ = 7.1 S_xx = 1750 S_xy = 36.45 S_yy = .78 Determine the proportion of variation in y that is explained by linear regression. Round your answer to three decimal places.

Consider the following data set A) Determine the fitted line B) Use the fitted line to predict the value of y when x = 3.5.

Data are recorded at one ACM on the total time to wait in line and then complete a transaction y(minutes) and the number of persons, x, already in line. A) Determine the equation of the least squares regression line. Round your answer to three decimal places. B) Estimate the time to finish your transaction when 6 people are ahead of you. Round your answer to three decimal places. C) Give a 95% prediction interval for the time to finish your transaction when 6 people are ahead of you in line. Round your answer to two decimal places.

Identify the values of the parameters A) β₀, B) β , and C) δ in the statistical model Y = -14 + 15 x + e where e is a normal random variable with mean 0 and standard deviation 7.