a. Assume the following regression modelwhere EiY₁ = B₁1X₁1 + B₂X₁2 + €į, i=1,...,niidN(0, o²), σ > 0 holds true. Suppose thatΣX1X2 = 0.2Show that the least squares estimators ₁ and ₂ from the multiple regression are thesame as if we were to fit separate, simple regressions on X₁ and X₂. b. Consider the following functions of the random variables X₁, X2, X3, and X4:· [X1 + X2 + X3 + X4]Y₁=1Y2 = [X₁ + X2] - [X3 + X4]2(i) State the above in the matrix notation.(ii) Find the expectation of the random vector Y(iii) Find the variance-covariance matrix of Y == Y₂H

Note: The problem has multiple questions As per the guidelines of the Q&A only the first…

Answered: a. Assume the following regression…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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?
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
Find the least square regression line.
1. Consider two least-squares regressions and y = Xíễ tế y = Xí$i+ XzB2 tê Let R2 and R2 be the R-squared from the two regressions. Show that R22 R2.
Over the years Olympic racers have been getting fasterin most events, and the women’s singles 500-meter kayakrace is no exception. A scatterplot displaying the data foryears since 1948 (x) and time in seconds (y) suggests thata linear model is appropriate. The equation of the leastsquares regression line is, yn = 144.627 - 0.776x, andr2 = 0.932.a) Interpret the value of r2 in this context.b) Compute and interpret the value of r in context.c) The Olympics are held every 4 years. What changein the winning time does this model predict from oneOlympics to the next?d) The residual for the winning time in 1980 was-1.795 seconds. Find this gold medal time.
Need only handwritten solution only (not typed one).
A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.
Find the quadratic regression curve through the following points (2, 5), (3, 5), (5, 3) y = 3.0000x? 0.3333x + 1.6667 y = 3.0000x2 + 1.6667x – 0.3333 O y = -0.3333x2 + 1.6667x + 3.0000 O y = 1.6667x2 – 0.3333x + 3.0000

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