The following data represents the rate of return of the stock exchange (x) and the rate of return of a certain stock (y). The equation of the least squares regression line is y =0.9764x +0.5975 and the standard error of the estimate is 2.3518. Answer parts (a)(d). 0.23 0.94 1.21 -0.57 -0.59 5.89 1.40 3.86 3.25 -2.53 1.89 -1.91 -2.01 3.00 0.90 O 5.90 -2.58 0.06 1.78 0.06 5.79 -1.57 (a) What is the mean rate of return for the stock if the rate of return of the S&P 500 is 4.24%? y=% (Round to one decimal place as needed.) (b) Construct a 90% confidence interval about the mean rate of raturm of y if x-4.24%. Lower Bound Upper Bound 1% (Round to one decimal place as needed.) (c) Predict the rate of return of the stock if the rate of return on the S&P 500 for a randomly selected month is 4.24%. y-D% (Round to one decimal place as needed.) (d) Construct a 90% prediction interval about the rate of return of y if x 4.24% Lower Bound Upper Bound peeded

The following data represents the rate of return of the stock exchange (x) and the rate of return of a certain stock (y). The equation of the least squares regression line is y =0.9764x +0.5975 and the standard error of the estimate is 2.3518. Answer parts (a)(d). 0.23 0.94 1.21 -0.57 -0.59 5.89 1.40 3.86 3.25 -2.53 1.89 -1.91 -2.01 3.00 0.90 O 5.90 -2.58 0.06 1.78 0.06 5.79 -1.57 (a) What is the mean rate of return for the stock if the rate of return of the S&P 500 is 4.24%? y=% (Round to one decimal place as needed.) (b) Construct a 90% confidence interval about the mean rate of raturm of y if x-4.24%. Lower Bound Upper Bound 1% (Round to one decimal place as needed.) (c) Predict the rate of return of the stock if the rate of return on the S&P 500 for a randomly selected month is 4.24%. y-D% (Round to one decimal place as needed.) (d) Construct a 90% prediction interval about the rate of return of y if x 4.24% Lower Bound Upper Bound peeded

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Suppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading. Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂ when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…
The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squares
The following table shows the marks in statistics and economics for ten students. Fit a least square line to the data using a) ‘X’ as the independent variable b) What will be the regression equation if X= 20
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. Use the method of least squares to compute an estimated regression line between sales and advertising. If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars. What does the slope of the estimated regression line indicate?
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and gathers the following data a. Construct a scatter plot. b. Use the least-squares method to determine the regression coefficients b0 and b1 c. Interpret the meaning of and in this problem. d. Predict the monthly rent for an apartment that has 1,000 square feet
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas use y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65F) over a 23-month period. He then computed the least squares regression line for predicting y from x and found it to be, ŷ=85+16x How much, on average, does gas used increase for each additional degree-day? The predicted amount of gas used when the outside temperature is 20 degree- days.
The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for 5 randomly selected states in the United States. Compute the least-squares regression line for predicting math proficiency from reading proficiency. State Percent Proficientin Reading Percent Proficientin Mathematics Illinois 75 70 North Carolina 71 73 California 60 59 Georgia 67 64 Florida 66 68 Send data to Excel The equation for the least squares regression line is y = . Round the slope and y -intercept to four decimal places as needed.
The Heights and Weights of 500 preschoolers have correlation r=0.52. The average height is 30.12 Inches, the average weight is 40.90 Pounds, the standard deviation of their heights is 4.16 inches, and the standard deviation of their weight is 6.42 Pounds. 1. What is the equation of the least squares regression line for predicting their weights from their heights? 2. I'm 35 Inches Tall- Predict my weight.
A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?