Exam 11: Regression Analysis I

The price y (in cents) of a domestic long distance telephone call is given by y = 2x + 25 where x denotes the number of minutes that the call lasts. A) What is the price, in dollars, of a 33 minutes call? B) If the telephone company charged you $3.33 for a domestic long distance call, how long was that call?

Consider the data (a) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀. (b) Estimate the error variance. (c) Obtain a 95 % confidence interval for $\beta$ ₁. Can you conclude that the slope is different from 0? (d) Determine the proportion of variation in y explained by x.

Consider the data set Calculate the (a) sample means (b) S_xx , S_xy , S_yy (c) Calculate the least squares estimates β1 and β0. (d) Calculate the sample correlation coefficient.

The letter x usually represents the independent variable, also called predictor variable

The total number of hours worked by a student, y, last week depends on the number of days, x, they worked. Data on twenty-eight students produce the summary statistics n = 28 $\bar{x}$ = 3.21 $\bar{y}$ = 14.79 S_xx = 2260.714 S_xy = 1969.286 S_yy = 2076.714 Determine the proportion of variation in y that is explained by linear regression. Round your answer to three decimal places.

A basketball fan collected data on the number of points per game, y, of her favorite player, associated with the number of minutes, x, played per game Given that S_xx = 189.50, S_xy 317.50, and S_yy 581.50, calculate the residual sum of squares S.S.E.

Consider the following data set: where S_xx = 10 , S_xy = 25, and S_yy = 74.Construct a 90% confidence interval for the intercept $\beta$ ₀. Round your answer to three decimal places.

Under the linear regression model, determine the (A) mean and (B) standard deviation of Y, for x = 12, when β₀ = 6, β₁ = 5, and δ = 7.

A recent graduate moving to a new job, collected a sample of rent (dollars) and size (square feet) of 2-bedroom apartments in a desirable area of the city. The data have the summary statistics We randomly selected 12 countries, of about 200 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 = 8 $\bar{x}$ = 1072.25 $\bar{y}$ = 1421.25 S_xx = 230081.5 S_yy = 217237.5 S_xy = 212376.5 Determine the equation of the best fitting straight line. Round your answer to three decimal places.

The Human Development Index (H.D.I.) provides a composite measure of three dimensions of human development: life expectancy, adult literacy, and income. One county's H.D.I. trend is shown below. A) Determine the equation of the least squares regression line. B) Estimate the H.D.I. in year 6.5. C) Construct a 95% confidence interval for the response in part B. Round your answer to three decimal places.

Consider the following information: n = 19 $\bar{x}$ = 9.959 $\bar{y}$ = 0.6679 S_xx = 1173.45 S_xy = 20.480 S_yy = 0.41771 A) If x is the predictor variable, determine the proportion of variation in y, that is explained by linear regression. B) If y is the predictor variable, determine the proportion of variation in x, that is explained by linear regression. Round your answers to three decimal places.

Consider the following linear regression model Y = β₀ + β₁x + e where β₀ = 4, β₁ = -2, and the normal random variable e, has the standard deviation 3. A) What is the mean of the response Y when x = 8? B) Will the response at x = 9 always be larger than that at x = 8? Answer "Yes" or "No".

Data on the number of cans of beverage served, y , and the number of students, x, attending a TV watching party were recorded on six occassions A) Calculate $\bar{x}$ B) Calculate $\bar{y}$ C) Calculate S_xx D) Calculate S_yy E) Calculate S_xy Calculate the least squares estimate G) Calculate the least squares estimate

Data on the number of cans of beverage served, y , and the number of students, x, attending a TV watching party were recorded on six occassions Find the value of . Round your answer to three decimal places.

Temperature anomaly means a departure from a reference value, usually obtained by a long-term average. A positive anomaly indicates that the observed temperature was warmer than the reference value. The following table shows the annual anomalies for the highest temperatures in six recent decades.. A) Obtain the last squares fit of year to the predictor temperature anomaly. B) Calculate the residual sum of squares. C) Estimate . Round your answers to three decimal places.

Consider the data (a) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀. (b) Estimate the error variance. (c) Obtain a 95 % confidence interval for $\beta$ ₁. Can you conclude that the slope is different from 0? (d) Find a 95% confidence interval for the mean response when x = 8.

Which of the following statements is (are) true? III) The point ( $\bar{x}$ , $\bar{y}$ ) lies on the fitted regression line

Consider the line y = -6 + 14x A) What is its intercept? B) What is its slope?

Consider the data set Calculate the (a) sample means. (b) S_xx , S_xy S_yy. (c) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀. (d) Estimate the error variance. (e) Determine the proportion of variation in y explained by x.

Consider the following data set. where S_xx = 10, S_xy = 16, and S_yy = 26.8. Construct a 95% confidence interval for $\beta$ ₁ . Round your answer to two decimal places.