The electricity generation problem: Most of S.As power stations are coal- fired. Assume a random sample of 10power stations were selected and their coal usage and electricity generated 2017 was obtained.Coal used in 2017(in million tonnes)15 6 10 18 9 7 14 11 5 8Electricity generated(million kilowatt hours)35 18 24 32 24 20 32 29 14 22Find the straight-line regression function to estimate electricity generated (y) from coal used (x) by the method of least squares.O A. 9=5.763+ 2.815xO B. =9.367+1.51&rOC.f=9.367+1.518yO D.f=5.763+2.815y

Given that, the ordered pairs are, x y 15 35 6 18 10 24 18 32 9 24 7 20 14 32 11…

Answered: The electricity generation problem:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. A Ross MAP team is trying to estimate the revenues of major-league baseball teams during the regular season using a regression model. Currently, the independent variables include stadium capacity, the number of weekend games, the number of night games, and the number of Wins (out of 162 regular season games). One of your team members suggests that the model also should include the number of losses as it provides additional explanatory power. Assume that ties are not possible; so every game results in exactly one team winning and the other team losing. Which of the following statements is the most likely conclusion of the new regression model? (a) R2 will increase, adjusted R2 will decrease, and Serror will decrease. (b) R2 and adjusted R2 will increase, and serror will decrease. (c) R, adjusted R2, and Serror will increase. (d) We cannot trust the regression output as some variables are highly correlated, resulting in multicollinearity. Answer to Question 3:
A market study found that the sales for a firm were related to advertising expenditure, as follows: Advertising Expenditure (Kshs ‘000’) Sales (Kshs ‘000’) 0 13 1 16 2 14 3 22 4 17 5 21 6 26 Required Draw a scatter diagram with the line of best fit to show the relationship. Determine the regression line equation for estimating the sales for a given level of advertising expenditure What is the estimated sale in thousand, if no advertising expenditure is incurred?
The following table shows the starting salary and profile of a sample of 10 2 p employees in a certain call center agency. Run a multiple regression analysis with starting salary as the dependent variable (pesos) and GPA, years of experience and civil service ratings as the independent variables. Use .05 level of significance.What is the computed R square of the resulting multiple linear regression and its interpretation? * Civil Years of Starting salary GPA service experience ratings 79.5 15000 80.1 15000 81.2 78.0 15500 81.3 79.0 16000 82.4 80.0 16200 83.4 85.0 17500 87.9 89.9 89.1 18000 90.3 16,300 84.2 17000 87.0 17900 88.1 84.1 89.0 89.2 R squared = 0.8053; This means that 80.53% of the total variation in the starting salary can be explained by its linear relationship with GPA, years of experience and civil service ratings. R squared = 0.9651; This means that 96.51% of the total variation in the starting salary can be explained by its linear relationship with GPA, years of…
8. You collect data on people's height and study the relationship between gender and height. A regression of the height on a binary variable (Female), which takes a value of one for females and zero otherwise, yields the following result: Height = 71.0- 4.84 x Female, R2 = 0.40, SER = 2.0 (0.3) (0.57) (a) What is the sample average male height? (b) What is the sample average female height? I (c) How to interpret the slope coefficient -4.84? (d) Is the error term in the regression more likely to be heteroskedastic or homoscedastic? Why? R English (United States) D'Focus Page 9 of 10 920 words 100%
12 young batsmen practiced batting at the nets for varying periods of time, and their dot ball percentage was calculated at the end of the month: a) Find the relationship between dot ball percentage and practice time per month using a scatter diagram and interpret. b) Find correlation coefficient and comment. c) Fit a least square regression equation (line) of dot ball percentage on practice time per month and comment. d) What will be the dot ball percentage when practice time per month is 32hr? e) Comment on the regression equation and explore how well it fits.
The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y. Mathematics score (X) 70 92 80 74 65 83 English score (Y) 74 84 63 87 78 90 ∑x=464, ∑y=476,∑x^2=36354,∑y^2=38254, ∑xy=36926. Estimate the regression parameters and also write the prediction equation.
School administrators wondered whether class size and grade achievement (in percent) were related. A random sample of classes revealed the following data. Number 10 8. 20 18 6. of Students 15 Average Grades 85 90 82 80 84 92 (%) 1. Calculate the linear correlation coefficient (Rc all answers to TWO decimal places) 2. Calculate the coefficient of determination (Rou all answers to TWO decimal places) 3.The linear regression equation is ASUS VivOBook
A company sets different prices for a particular DVD system in eight differentregions of the country. Table 1 shows the numbers of units sold and thecorresponding unit prices (in U.S. Dollars).Table 1: Sales DataRegion Sales (Units) Price (U.S. Dollars)1 420 1042 380 1953 350 1484 400 2045 440 966 380 2567 450 1418 420 109You are given the following regression model:Salesi = 1 + 2Pricei + uiwhere i is region, Sales are number of units sold, Price is unit price inU.S. Dollars, and u is a random error term.Based on the data:1. Estimate the regression model. 2. Interpret the estimated regression equation. 3. Compute the standard errors of the estimated coefficients. 4. Test the statistical significance of 2 at the 5% level of significance.5. Compute R2 and interpret it.
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual model…

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