Two variables are defined, a regression equation is given, and one data point is given.Study =Grade =Grade =Part 1number of hours spent studying for an examgrade on the examThe data point is a student who studied 10 hours and received an 81 on the exam.41.1 +3.6(Study)(a) Find the predicted value for the data point and compute the residual.Enter the exact answers.Residual = iPredicted value = i

Given Y-cap= 41.1+3.6(Study) The data point is a student who studied 10 hours and received an 81 on…

Two variables are defined, a regression equation is given, and one data point is given. Study = number of hours spent studying for an exam Grade = grade on the exam Grade = The data point is a student who studied 10 hours and received an 81 on the exam. Part 1 41.1 +3.6(Study) (a) Find the predicted value for the data point and compute the residual. Enter the exact answers. Predicted value = Residual = i i

Two variables are defined, a regression equation is given, and one data point is given. Study = number of hours spent studying for an exam Grade = grade on the exam Grade = The data point is a student who studied 10 hours and received an 81 on the exam. Part 1 41.1 +3.6(Study) (a) Find the predicted value for the data point and compute the residual. Enter the exact answers. Predicted value = Residual = i i

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 16CR: XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ...

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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?
XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation as ˆ y = 14 + 0.5 x y ^ = 14 + 0.5 x where y is the final-exam score and x is the score on the first test. Andrea scored 75 on the first test. What is the predicted value of the Andrea's score on the final exam? Andrea scored 56.5 on the final exam. What is the value of the residual?
A simple linear regression model was created to examine the relationship between the age of patients (i.e. the independent variable) and the patients' scores on a questionnaire that measures quality of life (i.e. the dependent variable). There were n=20 patients in the study, and some of the results of the regression are presented below: Estimated intercept = 42 Standard error of the intercept = 13.6 Estimated slope = -0.64 Standard error of the slope = 0.52 Based on these results, which of the following can we conclude, based on an alpha level of 0.05 for significance? Question 16 options: The intercept is not significantly different from 0, but the slope is significantly different than 0. Thus, we have mixed results and we cannot make a definitive statement about the significance of the association. There is a significant association, because the intercept is statistically significantly different than 0 (p<0.05). There is not a…
Use the regression identity for multiple linear regression to show that R2 =1- SSE/SST. a. Explain why this formula shows that the coefficient of multiple determination can also be interpreted as the percentage reduction in the total squared error obtained by using the regression equation instead of the mean,y~, to predict the observed values of the response variable. b. Referring to , what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed prices to predict the observed prices? c. Referring to , what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed graduation rates to predict the observed graduation rates?
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = β0 + β1x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: = 74.80 + 19.84 xGive a practical interpretation of the estimate of the slope of the least squares line. For a house with 0 rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the appraised value to increase $74,800. For each additional room in the house, we estimate the appraised value to increase $19,840. For each additional dollar of…
Researchers used weight in Kilograms (Y) as a dependent variable and Lean Body Weight (X1) and Mean Daily Caloric Intake (X2) as independent variables. a. Is the coefficient of Mean Daily Caloric Intake statistically distinguishable from 0? b. Perform a hypothesis test. c. Write the regression equation based on the results d. What is the predicted value of the weight of an obese girl if her lean body weight is 50.0 and mean daily caloric intake is 2000? e. What assumptions must be made in this experiment? Are they satisfied? f. Calculate the R2 value? Interpret it. g. Would you recommend the model? Why or why not?
2. A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x1), the number of meals eaten outside (x2), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. Coefficients Standard Error Intercept 450.08 53.6 x1 49.92 9.6 x2 10.12 2.2 x3 -.60 12.0 ANOVA df SS MS Regression 3078.39 1026.13 Residual (Error) 2013.90 95.90 Total d. What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? Additionally, test whether or not there is a significant relationship between the…
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 125 and a y-intercept of −390.Complete parts (a) and (b) below. a. What is the equation of the regression line? b. What does the symbol y represent? A. The symbol y represents the predicted value of price. B. The symbol y represents the expected price when the hotel's rating is 0. C. The symbol y represents the average price of hotels in the area. D. The symbol y represents the amount that price increases with a 1-point increase in rating.
A researcher found a linear correlation between course grades and the average number of hours spent on a mobile phone each day. The line of best fit has equation y ^ = 3.7 − 0.786 x with correlation coefficient r = − 0.84. a. Does this prove that spending too much time on a phone causes students to get lower grades? b. What does the regression line predict your final grade in a course will be if you spend an average of 150 minutes per day on your phone?