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- Fit these three regression models and then discuss the similarities and differences between them, particularly as relates to slope estimates (use CI’s) and R2. Also address why this is a “special case” and we wouldn’t necessarily expect to see these model characteristics for a typical dataset. a) Additive model including both predictors (output attached) b) Model including only Moisture (output attached) c) Model including only Sweetness BrandLiking = 68.62 + 4.38 Sweetness Term 95% CI P-ValueConstant (50.16, 87.09) 0.000Sweetness (-1.46, 10.21) 0.130 S R-sq R-sq(adj)10.8915 15.57% 9.54%A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. Data were collected that show the number of new customers added during each quarter between 2015 and 2018. A multiple regression model was developed with the number of new customers as the dependent and the following four independent variables: Period (1, …, 16): A variable that measures the trend; Q1 = 1 for first quarter, Q1 = 0 otherwise; Q2 = 1 for second quarter, Q2 = 0 otherwise; Q3 = 1 for third quarter, Q3 = 0 otherwise. Questions: 1. Explain each of the four slopes (Period, Q1, Q2, Q3). 2. How many new customers would you expect in the second quarter of the following year (2019)?Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05. a) Using technology, construct a regression model using all three independent variables. y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4 b) Test the significance of each independent variable using a= 0.10. c) interpret the p-value for each independent variable. d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning. e) Using the results from…
- The age (in weeks) and the number of hours slept in a day were recorded for arandom sample of 8 infants.Age (in weeks) 5 10 15 22 26 36 42 47Hours slept ina day14.9 14.5 14.7 14.2 13.4 14.1 13.4 13.7(a) Find the regression line that predicts the number of hours an infant sleeps ina day based on its age (in weeks).(b) How well does the regression line fit the data? Use words and statistics tosupport your answer.(c) Predict the number of hours that a 30-week-old infant would sleep in a day.Use words to state your answer.4. Housing Prices in New YorkWe have looked at predicting the price (in s) of New York homes based on the size (in thousands of square feet), using the data in HomesForSaleNY. Two other variables in the dataset are the number of bedrooms and the number of bathrooms. Use technology to create a multiple regression model to predict price based on all three variables: size, number of bedrooms, and number of bathrooms. Price Size Beds Baths 145 1.3 3 1.5 875 2.9 7 3.75 300 1.5 3 2.5 370 1.1 2 1 268 1.5 2 2 1399 4.8 6 5 1125 3.1 3 2.5 299 1.4 3 2 110 1.2 3 1 2999 6 7 8 170 1 2 1 269 1.5 3 1.5 150 1 2 1.5 288 1.8 3 2.1 350 1.3 3 2 120 0.9 1 1 309 2.4 4 2.5 1500 1.5 2 1.5 635 2.5 4 2.5 350 0.9 2 1 459 1.8 4 2.5 275 2.9 4 1.5 275 1.8 3 2 2500 3.7 3 3 187 1.4 3 1.5 238 1.7 3 1.5 155 0.7 1 1 175 1.6 3 1.5 569 3.2 4 2 105 1.2 2 2.5 a) Which of the variables which are significant at the 5% level? b) Which variable is the most…4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.
- Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage Annual (hours) Maintenance Expense 15 22 12 27 22 35 30 42 34 52 19 36 26 38 33 44 42 57 40 45 a. Develop the estimated regression equation that relates annual maintenance expense (in hundreds of dollars) to weekly usage hours (to 3 decimals). Expense = Weekly Usage b. Test the significance of the relationship in part (a) at a 0.05 level of significance. Compute the value of the F test statistic (to 2 decimals). The p value is Select your answer- - Select your answer What is your less than 0.01 between 0.01 and 0.025 - Select your a between 0.025 and 0.05 c. Jensen expe between 0.05 and 0.10 greater than 0.10 sed 30 hours per week.…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.…The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + bjx, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.5 1.5 2.5 3 4 4.5 6 Overall Grades 89 86 81 79 72 67 62 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.