The following table indicates the ages of a sample of female employees of People Plus Pty, and the corresponding monthly income of each employee (in thousands of Rands). Age In Years (x) Monthly Income (RO00s) (y) 40 43 49 49 32 36 27 31 38 41 46 42 3y completing the table given below, and then applying the relevant formulae, determine the linear regression function for this bivariate data set. y x2 ху ТОTAL If a female employee is 39 years of age, estimate her monthly income.
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- 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?The following table indicates the ages of a sample of female employees of People Plus Pty, and the corresponding monthly income of each employee (in thousands of Rands). Age In Years (x) 404932273846 Monthly Income (R000s) (y) 434936314142 By completing the table given below, and then applying the relevant formulae, determine the linear regression function for this bivariate data set. X Y X^2 XY TOTAL If a female employee is 39 years of age, estimate her monthly income.Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi-fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P14_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semi-fragile cargo.
- The following results are from data concerning the amount withdrawn from an ATM machine based on the amount of time spent at the ATM machine (SECONDS) and the gender, FEMALE (dummy variable = 1 for females and = 0 for males) and an interaction term, SECONDS*FEMALE Based on the regression results, what is the predicted amount withdrawn for a male who spends 20 at the ATM machine? (please express your answer using 1 decimal places)Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual starting salary of an employee with a doctorate degree? (Someone with no work experience). $ What is the predicted bi-annual starting salary of an employee with a bachelor’s degree? (Someone with no work experience). $
- The following table gives the ages of female students in school and the corresponding Body Mass index (BMI) of 8 randomly selected students.(α=0.05) Age24223032211925 BMI27283029282726 Determine whether ages and BMI are significantly related.Determine the coefficient of linear determination and Intepret.Set up a linear regression equation to predict body mass index from age of students.Predict the body mass index of student who has the age of 26 years.It is required to use the data given in the table to estimate the parameters of the simple linear regression equation by any of the estimation methods:Suppose the regression in Equation is estimated using LoSTR andLoEL in place of HiSTR and HiEL, where LoSTR = 1 - HiSTR is anindicator for a low-class-size district and LoEL = 1 - HiEL is an indicatorfor a district with a low percentage of English learners. What are thevalues of the estimated regression coefficients?
- The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x�^=�0+�1�. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.050.05 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 3939 2525 1515 4242 4242 2424 3232 2020 3030 3737 Snow Accumulation (in.in.) 66 1515 2929 66 1414 2626 2323 1212 1616 77 Copy Data Regression equation: yˆ=�^= Is the equation appropriate? YesThe data in Table 11.17 are given for 9 patients with aplastic anemia [11]. 11.6 Test for the statistical significance of the regression line using the t test.For variables x1, x2, x3 and y satisfying the assumptions for multiple linear regression inferences, the population regression equation is y = 27 – 4.7x1 + 2.3x2 + 5.8 x3. For samples of size 20 and given values of the predictor variables, the distribution of the estimates of β1 for all possible sample regression planes is a _________ distribution with mean _________ and standard deviation _______.