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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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…
The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of the company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below. 4. Perform an F test and determine whether independent variable and dependent variable are related. Fully interpret the meaning. Use α = .05 5. Conduct Residual Analysis and fully interpret the meaning. 6. If on a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 10 million, what would you expect the price of the stock to be? GRAPH IS SHOWN BELOW
Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. What can you say about the strength of this relationship? Carry out a test to determine whether y is…
1. Explain the purpose or use of the following:a. Linear regression equationb. Correlation coefficient.
19
Do the following plots show 1. Constant variability 2. Nearly normal residuals 3. Independent observations for SLR (conditions for linear regression)
4. Residuals are... the difference between observed and values the model. B. data collected from individuals that is not consistent with the rest of the group. C. none of these D. possible models not explored by the researcher. E. variation in the data that is explained by the model. 5. If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)? A. b will increase, and r will decrease. b will decrease, and r will increase. C. both will decrease. D. both will increase. E. both will remain the same. 6 An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches. Their model is: # cheerios = 0.56 +5.11(diameter). The slope of this model is best interpreted in context as... A. For every 5.11 inches of diameter, the circumference is about 1 cheerio bigger. B.…
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.
3. Regression analysis breaks scores on the DV into... (explain and give equations)

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