Q5/ A: Use Linear Regression to fit the following experimental data X 3 2 3 1 6 Y 1 2 10 9 8 05 5 10
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- FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average, measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is ŷ = 2,671,134.68 +684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. Residual $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 -$5,000,000 -$10,000,000 -$15,000,000 4 ITS % 6 MacBook Pro ● 8 ● ● ● 10 12 14 Scoring Average (Points per Game) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game. 16 tv…Newton's Divided DifferenceWhich of the following is true of a linear regression line? a. Located as close as possible to all the points of a scatter chart. B. Is defined by an equation having 2 parameters: the slope and the intercept c. Provides an approximate relationship between the values of two parameters d. All of the above
- The following data shows memory scores collected from adults of different ages. Age (X) Memory Score (Y) 25 10 32 10 39 9 48 9 56 7 Use the data to find the regression equation for predicting memory scores from age. The regression equation is: Ŷ = 4.33X + 0.11 Ŷ = -0.11X + 4.33 Ŷ = -0.11X + 13.26 Ŷ = -0.09X + 5.4 Ŷ = -0.09X + 12.6 Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 28 For the calculations, leave two places after the decimal point and do not round: Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 43 For the calculations, leave two places after the decimal point and do not round: Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 50 For the calculations, leave two places after the decimal point and do not round:Q.1/ Use linear regression to fit the following experimental data. 图 2 3 4 5 7 10 y 5.2 7.8 10.7 13 19.3 26.5A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:
- The percentage of adults who smoke in America is given below. Year America 1970 37.4 mon n 1980 33.2 1990 25.3 2000 23.1 2010 19.4 a) Write the linear regression model for A(x), representing the percentage of adult smokers in America x years since 1970. [Use your calculator OR Desmos to find the equation, Round coefficients to the nearest 100"] b) What is the slope of A(x)? Explain its meaning. c) Solve A(x) = 15. Show your work. Explain the meaning of your answer. d) Suppose in 2005, there were approximately 200 million adults in America. Use your model to estimate how many were smokers. Show how you get your answer.The following data on x maternal age in years of the young birth mothers and y = weight of baby born in grams summarizes the result of a study. Assume that a simple linear regression model y = Bo + B1x + e is an appropriate model for the study. x-bar = 17 (avg of x's) y-bar = 3004.1 (avg of y's) SSx = 20 SSxy %3D 4903 SSw 1539182.9 n 10 Calculate the value of s-(standard error of regression) and enter the answer to the nearest tenth (1 decimal place).Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time needed for the joint to set (measured in hours) as it is related to the temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R2 = 0.965 to answer the following questions. 1. Find the equation of the regression line. 2. Interpret the slope in the words of the problem. 3. Find the Coefficient of Determination and interpret in the words of the problem
- B b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between a = average number of passing yar and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the avera passing yards per attempt. Enter negative value as negative number. WinPct =| |)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately So, for every increase : of one yar number of passes per attempt, the percentage of games won by the team increases by %. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 5.5. Use th regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs.…Use the p-value criterion to find the best model for predicting the number of points scored per game by football teams using the accompanying National Football League Data. Does the model make logical sense? E Click the icon to view the National Football League Data. Determine the best multiple regression model. Let X, represent Rushing Yards, let X, represent Passing Yards, let X3 represent Penalties, let X4 represent Interceptions, and let Xg represent Fumbles. Enter the terms of the equation so that the Xy-values are in ascending numeral order by base. Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to three decimal places as needed.) Points/Game =+ OX 01+Og+O1 A. OB Points/Game = O C. Points/Game = OD. Points/Game = + Dx O E. Points/Game = Data table for the national football league Points/ Game Rushing Yards/ Game Passing Yards/ Penalties Interceptions Fumbles O Game 25.2 90.1 259.2 140 18 4 16.2 95.2 208.5 108…Tristan has completed his STAT 1342 course. He intends to build a simple linear regression model using control variable (X) as number of hours per week for his preparations and (Y) as the weekly performance measured in a 100-point scale and based on his self-assessment. There were totally n = 28 weekly collected records. The model built by Tristan was: Ý = 10 + 7· X with the standard error of estimated slope equal to SE = SE [6] = 2.8 1. At the significance level, a = 0.01, is there sufficient evidence that X positively impacts Y? • Evaluate Test Statistic • Specify critical value (or values) for this procedure • State the Rejection Rule • Formulate your decision 2. Estimate the population slope (= B) with confidence level, C = 0.95 • Specify critical value (or values) for this procedure • Evaluate UCL and LCL Solution 10
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