Two friends find themselves in a huge debate. One claims that if a regression model is to be constructed for demand for a good, price should be the independent variable, and quantity demanded should be the dependent variable. Hence, the regression should be as: 9. = 0, + 0,p, + u, where Q is quantity demanded and P stands for price. The other friend, on the other hand, states that the demand will affect the price; therefore the true regression should be formed as: P: = a, +a,9; +u, a) Show that 6,â =r², where r is the sample correlation coefficient between price and quantity. b) Show that the goodness of fit of the two fitted regressions is the same.

Two friends find themselves in a huge debate. One claims that if a regression model is to be constructed for demand for a good, price should be the independent variable, and quantity demanded should be the dependent variable. Hence, the regression should be as: 9. = 0, + 0,p, + u, where Q is quantity demanded and P stands for price. The other friend, on the other hand, states that the demand will affect the price; therefore the true regression should be formed as: P: = a, +a,9; +u, a) Show that 6,â =r², where r is the sample correlation coefficient between price and quantity. b) Show that the goodness of fit of the two fitted regressions is the same.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

You are the Filipino analyst hired by the multinational company to study the sales data of its more than 75 stores worldwide. You used regression analysis to predict $ sales (y) by using $ advertising (x1) and $ salary of sales representatives (x2) across all the branches. You obtained the following regression function: y = 7800 + 8.5x1-1.6x2 If the advertising budgets of one of the branches of the corporation is now $45,000 (which is 10% more than before) and the salary of sales representatives is now $8,500 (which is 20% less than before), then the predicted sales before in that branch is A. $376,700 B. $335,650 C. $417,750 D. $341,250
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1,000s) 96 90 ŷ = 95 92 95 94 94 94 Television Newspaper Advertising Advertising ($1,000s) ($1,000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let X₁ amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) ŷ = represent the (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly…
A new footwear manufacturer is trying to compete with the major brands by investing heavily in Research and Development (R&D). Their goal is to produce a premium lifestyle sneaker that is more comfortable, longer lasting and more stylish than any of their competitors. Below are some data on dollars spent on R&D and new customers acquired for the last 5 quarters. Regression Equation: Y= 0.5 + 1.35X New Customers R&D Dollars Acquired (in millions) (in thousands) 8 12 12 15 13 18 14 20 18 25 Based on looking at the numbers and/or sketching a scatter-plot, what conclusion can we draw about the data? The variables are negatively correlated You cannot tell until we perform some calculations There does not appear to be a strong correlation between the variables The variables are positively correlated
Jackson finds that the heavier a person is, the higher his pulse rate tends to be. A linear regression model he built suggests that 20-kilogram differences in weight correspond to differences in pulse rate of 5 beats per minute. Which of the following must be true and explain your answer. (I) The correlation coefficient between body weight and pulse rate is 1/4. (II) Your pulse rate slows down 3 beats per minute if your weight decreases by 12 kilograms.
You are the Filipino analyst hired by the multinational company to study the sales data of its more than 75 stores worldwide. You used regression analysis to predict $ sales (y) by using $ advertising (x1) and $ salary of sales representatives (x2) across all the branches. You obtained the following regression function: y = 7800 + 8.5x1-1.6x2 If the advertising budgets of one of the branches of the corporation is the same as before and the salary of sales representatives is now 20% less than before, then the predicted sales in that branch will A. increase B. no sufficient information to determine C. decrease D. remain the same
Consider the simple linear regression model Wage = Bo + B1*Age + U. The error term U can capture the followings, with the exception of O A. possible measurement error in Wage. O B. the temperature in London Ontario tomorrow. O C. possible model misspecification, such as the nonlinear effect of Age on Wage. O D. other variables that affect the dependent variable, such as previous work experience.
Suppose that the table shows the COVID-19 cases and deaths in some NCR cities during the COVID-19 surge. COVID-19 cases (X) COVID-19 deaths (Y) 820 8 560 6 470 2 onship 680 4 660 5 1100 15 c. How do you interpret the slope of the estimated simple linear regression model which describes the linear relationship between COVID-19 cases (x) and COVID-19 deaths (y)? ✓ [Select] There is an expected increase of 7 in y for every unit increase in x. There is an expected increase of 0.019 in x for every unit increase in y. There is an expected increase of 0.019 in y for every unit increase in x. There is an expected increase of 7 in x for every unit increase in y. >
The registrar at State University believes that decreases in thenumber of freshman applications that have been experiencedare directly related to tuition increases. They have collectedthe following enrollment and tuition data for the past decade: a. Develop a linear regression model for these data andforecast the number of applications for State Universityif tuition increases to $10,000 per year and if tuition islowered to $7000 per year.b. Determine the strength of the linear relationship betweenfreshman applications and tuition using correlation. c. Describe the various planning decisions for State Univer-sity that would be affected by the forecast for freshman applications.
If the equation of the regression line that relates income in dollars of student’s parents, xx, with cost in dollars of tuition,yy, is y=8500+0.018xy=8500+0.018x. a. What is the best prediction for the tuition of students whose parents earn no income? b. What is the best prediction for the tuition of students whose parents earn $45000? c. What is the best prediction for the tuition of students whose parents earn $80000?
If you know that the equation of the simple linear regression between the final exam result and the mid-year examination result for students in engineering statistics is as follows: Final exam = 50 + 0.5 x midterm according to the above equation, then the regression coefficient is:
In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that there is a positive correlation between x and y there is a negative correlation between x and y if x is increased, y must decrease None of the answers is correct.