2. Suppose we have a simple linear regression scenario:y = + Bir +eBut suppose it's a slightly unusual situation, in that:• By a strange quirk of fate, we know the value of Bo, so it does not need to be estimated.(We'll just leave it in the model as &, but it is a known value.)• The values of r are always positive, and our gut tells us that larger values of r provide lessreliable information about y, so when estimating we want to give them lower weight inthe estimation.We decide to estimate by choosing Bn to minimize:Derive the estimator of 31.

In this scenario, we are considering a simple linear regression model where the relationship between…

Answered: 2. Suppose we have a simple linear…

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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Management proposed the following regression model to predict sales at a fast-food outlet. y=B₁ + B₁x₁ + B₂x₂ + Bzx3 +6 where x₁ = number of competitors within one mile X₂= population within one mile (1,000s) x3 = [1 if drive-up window present lo otherwise y = sales ($1,000s). The following estimated regression equation was developed after 20 outlets were surveyed. 9-10.1-4.2x₁ + 6.8x₂ + 15.3x3 (a) What is the expected amount of sales (in dollars) attributable to the drive-up window? $ (b) Predict sales (in dollars) for a store with four competitors within one mile, a population of 8,000 within one mile, and no drive-up window. $ (c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and a drive-up window. $
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 10 9 7 8 5 4 4 Cups of coffee (n) 1 1 2 3 3 4 5 5 Unless otherwise stated, you can round values to two decimal places.a) Using regression to find a linear equation for P(n)P(n) = b) Interpret the meaning of the slope of your formula in the context of the problemc) Interpret the meaning of the P intercept in the context of the problemd) Use your model to predict the number of people that will complain about his attitude if he drinks 8 cups of coffee.(Round to 2 decimals) e) Is the answer to part d reasonable? Why or why not?f) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.
There may be an association between a country's birthrate and the life expectancy of its inhabitants. A report this past year, coming from a random sample of 20 countries, contained the following information: the least-squares regression equation relating the two variables number of births per one thousand people (denoted by x) and female life expectancy (denoted by y and measured in years) is y = 82.28 – 0.51 x, and the standard error of the slope of this least-squares regression line is approximately 0.35. Based on this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the…
1. Consider the following regression model: Fram Risk Score; = Bo + B1 × Health Insurance; + u¿ The Framingham Risk Score predicts 10-year risk of cardiovascular disease based on age, cholesterol levels, blood pressure, blood sugar, use of medication for high blood pressure, and smoking. A higher score means worse overall cardiovascular health. A researcher who collects data and regresses the Fram Risk Score against Health Insurance (= 1 if have insurance) finds that B, 2. Consider the following regression model: Class Average; = Bo + B1 x Office Hours; + u; Class Average is the students' average grade in the class at the end of the term and Office Hours is the number of office hours held by the instructor over the entire term. A researcher who collects data and regresses Class Average against Office Hours finds that, surprisingly, B V A V A
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: Cups of coffee (n) 1 1 2 3 4 5 5 People (P) 12 10 10 6 6 4 2 3 (a) Using regression to find a linear equation for P(n). Round to 2 decimal places. P(n)= (b) How many cups of coffee should he drink so that no one will complain about his attitude? Round to one decimal place.
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
3. Consider the following regression model: Weekly Hours = Bo + B1 × Wage + uj Weekly Hours is the average number of hours the individual worked over the course of the year and Wage is the individual's average hourly wage over the course of the year. A researcher who collects data and regresses Weekly Hours against Wage finds that B1 > 0. The OLS estimator, B, however, likely suffers from omitted variable bias because those individuals who earn high wages may be driven personalities who would work long hours no matter the wage. Because of this omitted variable bias, it is likely the case that B1_B1. A) В)
Can you please solve all parts of the question manually. Thank you!
1) You run the following regression: TS = B+B MALE + B MEDU +ß FEDU¸+ u. i 0 1 i 2 i 3 i where: TS - pupil's test score at the end of primary school, MALE - a dummy variable indicating if a child is a male (MALE=1) and equal zero otherwise, MEDU - mother's number of years of education, FEDU - father's number of years of education. You can test if mother's education has the same effect on child's test scores as father's education by: O A. running two t tests for the two hypotheses: B₁=0 and ₁=0. 2 O B. running two t tests for the two hypotheses: O C. running an F test for the hypothesis O D. running an F test for the hypothesis =B 3 ₁= ₂=0 and B₂=0. 2 ₁=B₁₂=B3
Consider the following linear regression prediction equation: Y = 12 + -1x. What is the direction of the relationship between these two variables? a. The relationship between the observed X and the predicted Y is negative. b. The relationship between the observed X and the predicted Y is positive. c. There is no relationship between the observed X and the predicated Y. d. There is a weak relationship between the observed X and the predicted Y with no direction.
suppose that the regression line is ỹ=2(x-4), then the predicted value of y when x = 3 is O -2 none O -4 O -6 O 2 O -1
1 Is it possible to identify the following equations with any standard equation referred in discussion relating two variable linear regression? If yes, write down the name of the equation. Otherwise write no. E (Y X)= a + BX+e Y= a+ BX+e Y = d +BX Y= d + B X+u E(Y | X)= d + (B ) X Y= d + (B ) X+u (Y ) = d + (B ) X+e Y= a+ BX+u %3D

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