(d) Let b and b be the least squares estimate of ẞ with and without the i-th observation included in the data, respectively. Show that b - b(¹)(1)where e₁ = y -hat(y), = y₁-xb is the i - th residual when fitted on the whole data.3Ćb-b(i)(X¹X) - ¹xiei1 - hiiwhere ei = Yi - ŷi = yi - ab is the i-th residual when fitted on the whole data.=1-h(d) Let b and b) be the least squares estimate of 3 with and without the i-th observation included in thedata, respectively. Show thati i

Given that b andb(i) are the least squares estimate of β with and without the ith observation…

Answered: (d) Let b and b(₁) be the least squares…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use a table to obtain the formula for the best least-squares fit to the data following data points: (1,2) (2, 3) (3,7) (4,9) (5, 12) Results from your Table ● Σα ● X = Συ · Σxy Σα2 Regression Line •y= - -
c) Give the expression of R˜^2 in terms of R^2 , and justify your answer.
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
Consider the data (1,3), (2,5), (3,9.67) (a) Derive the normal equations for the best fit of the form f(x) = - - + Dx? (b) Find C, D using the normal equations derived above and given data. (c) Find a suitable Linearization for f (x) =- + Dx² (Don't find C, D)
Find the least square regression line.
For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is
A researcher collects data between the age in years, (x), of a movie theater's popcorn popper and the cost of its monthly maintenance,(y).Find the regression equation. Round b to three decimal places.ˆyy^ = + CorrectxxFill in the table to find the residuals. Round table entries to three decimal places. xx yy ˆyy^ y−ˆyy-y^ 8 58 9 98 15 102 4 32 7 60 3 31 2 25 What is the correlation coefficient? Round to three decimal places. Graph the data and find the outlier. Give the ordered pair here:(, )If your ordered pair is actually the outlier, then the correlation coefficient would increase. Delete the ordered pair you chose and find the correlation coefficient again. Type the new correlation coefficient rounded to three decimal places here: Put the outlier back into your data and then find the test statistic, p-value, df, and critical value(s) for a test to find if there is a positive correlation with α=0.01α=0.01. Round to 3 decimal placestt…
For the linear regression model Y = bo + b1(X): The p-value for the intercept is large: about 0.98 The p-value for the slope is very small: less than 2 times 10^(-16) What can we conclude? Since the p-value for the intercept is large, we can conclude that there is not a strong correlation between X and Y. Since the p-value for the intercept is large, we can conclude that there is a very strong correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very weak correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very strong correlation between X and Y. We are not able to assess the strength of the correlation between X and Y with the output provided.
Civil engineers often use the straight-line equation, y = bo+b ₁x, to model the relationship between the shear strength y of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 resulted in a Coefficient of Determination of 0.7589. Given that r ²= 0.7589, give a practical interpretation of r 2, the coefficient of determination for the least squares model. In repeated sampling, approximately 75.89% of all similarly constructed regression lines will accurately predict shear strength. We expect about 75.89% of the observed shear strength values to lie on the least squares line. We expect to predict the shear strength of a triplet test to within about 0.7589 tons of its true value. About 75.89% of the total…
We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Adrian Beltre 104 32 18.000 Justin Smoak 34 14 3.900 Jean Segura 64 20 2.600 Justin Upton 87 31 22.125 Brandon Crawford 84 12 6.000 Curtis Granderson 59 30 16.000 Aaron Hill 38 10 12.000 Miquel Cabrera 108 38 28.050 Adrian Gonzalez 90 18 21.857 Jacoby Ellsbury 56 9 21.143 Mark Teixeira 44 15 23.125 Albert Pujols 119 31 25.000 Matt Wieters 66 17 15.800 Logan…
The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650

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(d) Let b and b(₁) be the least squares estimate of 3 with and without the i-th observation included in the data, respectively. Show that b-b(i): (XX)-¹xili 1-hii where e; = y₁ - yi = yi-b is the i-th residual when fitted on the whole data. =