2. Using the linear model ofy = Bo + Bi +,a researcher calculated the hat-matrix H and the residual e using 6 observations.H = X(X'X)−¹X' =[0.2516 0.1101 0.3931 0.0534 0.1101 0.08180.1101 0.2044 0.0157 0.2421 0.2044 0.22330.3931 0.1572 0.7704 -0.1352 0.0157 -0.05970.0535 0.2421 -0.1352 0.3176 0.2421 0.22330.1101 0.2044 0.0157 0.2421 0.2044 0.223270.2232 -0.0597 0.27990.08180.22330.2516_tattu. 1 Hat IS, usobentions wilMathe.sage(c) Identify observations with large standardized residual value.-aluei lalgt w....TYvilluaUL11.Jinta2e =-0.02]0.12-0.560.88-0.01-0.07 Standardized Residual• Detects outliers with respect to y• Labeled as "rstandard" in RHow to detect unusual y from the trend?Use the residual y¡ — ŷ¡ = e¡ (residual of ith observation)• For the best use, We need to standardize e; by dividing ei• By the matrix calculation, we can show that●Var (ei) = o² = 0² (1 - hii)Replacing ² by s² = MSE and taking the square root, we obtain%e₁ = √= √√s² (1 — hii) =) = s√√(1- -hii)• Then, ith standardized residual = r; is large ifeiri =·- | 20 | = 15√/₁² - ₁ />> 2.(Large

Observations with large standardized residual value have to be identified using the information…

Answered: (c) Identify observations with large…

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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Similar questions

In a multiple regression analysis involving an intercept, 15 independent variables and 200 observations, Total SS = 800 and Residual SS = 240. Adjusted R-squared is
5. A researcher measures how positive a person's mood is and how creative he or she is, obtaining the following interval scores. (a) Calculate the linear regression equation. (b) What is the predicted (Y') creativity score for anyone scoring 3 on mood? (c) What is the standard error of the estimate? (d) Interpret the standard error of the estimate for this relationship. Participant Mood X Creativity Y 110728639114645556377748 259 46 10 14
Can Discrete quantitative data provide reliable results?
Interpret the following graphs for multiple linear regression and comment on the validity of model assumptions
Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the neorest fire station. This information will be used in setting rates for insurance coverage. For o somple of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire domage, in thousands of dollars (y). ANOVA table Source Regression Residual SS df MS F 1,870.5782 1,870.5782 41.39 1,265.4934 3,136.0716 28 45.1962 Total 29 Regression output Standard Variables Coefficients Error t(df-28) Intercept Distance-X 13.76815 3.106 2.914 3.77es e. 5861 6.43 Click here for the Excel Data File a-1. Determine the regression equation. (Round your answers to 3 decimal places.) y3D X. a-2 Is there a direct or indirect relotionship between the distance from the fire station and the amount of fire damage? The relationship between distance and damage is b. How much domage would…
Seedlings of understory trees in mature tropical rainforests must survive and grow using intermittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Researchers experimentally irradiated seedlings of the Southeast Asian rainforest tree with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Below is the data. Fit a linear model to the data. Tree Mean Fleck (min) Relative growth rate (mm/mm/week 1 3.4 0.013 2 3.2 0.008 3 3 0.007 4 2.7 0.005 5 2.8 0.003 6 3.2 0.003 7 2.2 0.005 8 2.2 0.003 9 2.4 0 10 4.4 0.009 11 5.1 0.01 12 6.3 0.009 13 7.3 0.009 14 6 0.016 15 5.9 0.025 16 7.1 0.021 17 8.8 0.024 18 7.4 0.019 19 7.5 0.016 20 7.5 0.014 21 7.9 0.014 a)What is the rate of change in relative growth…
Do the following plots show 1. Constant variability 2. Nearly normal residuals 3. Independent observations for SLR (conditions for linear regression)
The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.

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