Construct a 95 % confidence interval for the slope of the regression line. Round your answers to two decimal places, if necessary. Heights of Fathers and Sons (in Inches) Height of Father, x Height of Son, y 71 71 74 75 67 67 68 72 68 70 75 75 70 70 72 71 72 72 Copy Data 囲 Tables E Keypad Answer Keyboard Shortcuts Lower endpoint: Unner endnoint:
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Using the regression results in column (3):a. Do there appear to be important regional differences? Use an appropriate hypothesis test to explain your answer.b. Juanita is a 28-year-old female college graduate from the South. Mollyis a 28-year-old female college graduate from the West. Jennifer is a28-year-old female college graduate from the Midwest.i. Construct a 95% confidence interval for the difference in expectedearnings between Juanita and Molly.ii. Explain how you would construct a 95% confidence interval forthe difference in expected earnings between Juanita and Jennifer.(Hint: What would happen if you included West and excludedMidwest from the regression?)The accompanying table lists systolic blood pressures (mm Hg) and diastolic blood pressures (mm Hg) of adult females. Find the (a) explained variation, (b) unexplained variation, and (c) prediction interval for a systolic blood pressure of 118 mm Hg using a 99% confidence level. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Systolic Diastolic 127 69 103 65 130 73 104 64 157 74 97 51 155 90 111 69 124 68 112 75 103 60 128 67
- A teacher conducted a regression analysis to investigate the relationship between student height and femur length. Computer output from the linear regression analysis is shown in the table. The analysis was performed on a sample of 24 students. Term CoefCoef SE CoefSE Coef Constant 28.34 0.945 Femur length 1.73 0.023 Assume that the conditions for inference for the slope of the regression equation have been met. Which of the following defines the margin of error for a 99.5 percent confidence interval for the slope of the least-squares regression equation? A)3.104 (0.023) B)3.104 (1.73) C)3.119 (0.023) D)3.119(0.945) E)3.119(1.73)The accompanying table lists systolic blood pressures (mm Hg) and diastolic blood pressures (mm Hg) of adult females. Find the prediction interval for a systolic blood pressure of 121mm Hg using a 99% confidence level. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Systolic Diastolic 125 69 104 65 129 75 108 65 157 74 95 53 155 89 110 69 120 69 115 73 101 59 127 67 The 99% prediction interval for a systolic blood pressure of 121mm Hg is ____mm Hg<y<___mm Hg.Sarah is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 7 2 2 9 3 3 9 4 4 10 3 5 11 5 6 12 3 Sarah would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The expected number of new clients per month for an employee who made 10 presentations per month is ________. 2.3982 1.6753 3.0521 3.4348
- Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with an altitude of 6327 ft (or 6.327 thousand feet). Altitude 2 8 13 23 28 31 32 Temperature 56 40 27 −1 −34 −41 −50 a. Find the explained variation. (Round to two decimal places as needed.) b. Find the unexplained variation. (Round to five decimal places as needed.) c. Find the indicated prediction interval. ______°F<y<______°FA random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The heart rate and maximal oxygen uptake were recorded for each player during a training session. A regression analysis of the data was conducted, where heart rate is the explanatory variable and maximal oxygen uptake is the response variable. If a 95 percent confidence interval is constructed for the slope of the population regression line, which of the following is a condition that must be checked? A)The true relationship between heart rate and maximal oxygen uptake is linear. B)The correlation between heart rate and maximal oxygen uptake is not equal to zero. C)The confidence interval is not biased. D).The point (x_,y_) falls on the regression line. The X and Y have a line on top. E)The slope is not equal to zero.A manager wishes to find out whether there is a relationship between the age of his employees and the number of sick days they take each year. The data for the sample follow. If the first letter of your last name starts with A to M, use level of significance 0.05, otherwise, if the first letter of your last name starts with N to Z, use level of significance 0.01. a. Draw/sketch a SCATTER PLOT with regression line and regression equation. b. State the null and alternative hypotheses. Ho (Null Hypothesis): Ha ( Alternative Hypothesis) c. Level of Significance d. Determine the degrees of freedom (df) and t critical value. e. Correlation coefficient (Pearson r). f. t statistic g. Compute the slope of regression line. h. Compute the mean of x and y i. Compute the intercept of regression line. j. Write the regression equation k. Write the complete interpretation of the results and conclusion.
- Based on the sample data and the regression line, complete the following. The managers of an electric utility wish to examine the relationship between temperature and electricity use in the utility's service region during the summer months. In particular, the managers wish to be able to predict total electricity use for a day from the maximum temperature that day. The bivariate data below give the maximum temperature (in degrees Fahrenheit) and the electricity use (in thousands of kilowatt hours) of electricity generated and sold for a random sample of summer days. A best-fitting line for the data, obtained from least-squares regression, is given by =y+83.852.67x, in which x denotes the maximum temperature and y denotes the electricity use. This line is shown in the scatter plot below. (a)For these data, values for electricity use that are greater than the mean of the values for electricity use tend to be paired with temperature values that are ▼(Choose one) the mean of…Bill is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 2 1 2 8 2 3 9 4 4 10 3 5 11 5 6 12 6 Bill would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The average number of new clients per month for an employee who made 20 presentations per month is ________. 5.02 5.45 3.43 8.69In Exercises, presume that the assumptions for regression inferences are met.Study Time and Score. Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise. x 10 15 12 20 8 16 14 22 y 92 81 84 74 85 80 84 80 a. Determine a point estimate for the mean test score of all beginning calculus students who study for 15 hours.b. Find a 99% confidence interval for the mean test score of all beginning calculus students who study for 15 hours.c. Find the predicted test score of a beginning calculus student who studies for 15 hours.d. Determine a 99% prediction interval for the test score of a beginning calculus student who studies for 15 hours.ExerciseApplying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.
