iven the following table, use the matrix method to derive the constant and slope parameters of the sample regression function: Productivity index = f(Daily sleep hours). X and Y stand for the daily sleep hours and productivity index respectively. X (Daily sleep hours) Y (Productivity index)(X first then Y in pairs so )X= 2 Y= 30 X=4 Y=35 X=5 Y=40 X=6 Y=65 X=8 Y=80

iven the following table, use the matrix method to derive the constant and slope parameters of the sample regression function: Productivity index = f(Daily sleep hours). X and Y stand for the daily sleep hours and productivity index respectively. X (Daily sleep hours) Y (Productivity index)(X first then Y in pairs so )X= 2 Y= 30 X=4 Y=35 X=5 Y=40 X=6 Y=65 X=8 Y=80

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

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
Given the following table, use the matrix method to derive the constant and slope parametersof the sample regression function: Module test mark = f (Weekly study hours). X and Y standfor weekly study hours and module test mark respectively. X (Weekly study hours) Y (Module test mark) 1 40 2 40 3 45 4 60 5 70 6 75
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.…
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 210 2,520 144 44,100 10 15.5 190 2,945 240.25 36,100 Total 151 1,750 2,312 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.627 3.173 2.877 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the…
Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+ε�=�+��+��+� Now suppose that the estimate of the model produces following results: α=344.585�=344.585, ba=0.106��=0.106, bp=−12.112��=−12.112, sba=0.155�ba=0.155, sbp=4.312�bp=4.312, R2=0.764�2=0.764, and F-statistic=12.593F-statistic=12.593. Note that the sample consists of 10 observations. According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures sales by approximately gallons. Similarly, a $1 increase in the selling price sales by approximately gallons. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining paint sales? Check all that apply. Selling price (P)…
For the regression model Yi = b0 + eI, derive the least squares estimator.
in the regression specification y =α+βx +δz +ε, the parameter α is called
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The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433x
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
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