Use R to find the multiple linear regression model. Based on the results or R, answer thefollowing questions:(a) Fit a multiple linear regression model to these data.(b) Estimate o².(c) Compute the standard errors of the regression coefficients. Are all of the modelparameters estimated with the same precision? Why or why not?(d) Predict the power consumption for a month in which x₁ = 75 F, x2 = 24 days,X3 = 90%, and x4 = 98 tons. 5. The electric power consumed each month by a chemical plant to thought to be relatedto the average ambient temperature x₁, the number of days in the month X2, theaverage product purity x3, and the tons of product produced x4. The past year'shistorical data are available and are presented in the following table.y240236270274301316300296267276288261X₁253145606572808475605038X₂242124252526252524252523X3919088879194878688919089X410095110889499979611010510098

This question focuses on using multiple linear regression to analyze data from a chemical plant in…

Answered: Use R to find the multiple 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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The table contains a subset of data published by the American Institutes for Research in 2013. These data specify the graduation rate of five different U.S. colleges and the instructional expenditure per student at each of the colleges. Use these data to answer the questions. (a) Generate the regression equation for predicting graduation rates from the expenditure per student. (b) Using the regression equation, predict the graduation rate for a school that spends $6800 per student. (c) Use the regression equation to determine how much a school would need to spend to obtain a 100% graduation rate.Table: Graduation Rate and Expenditure per Student College Expenditure/Student Graduation Rate Alaska University 10,540 46.2 Arizona State University 8836 57.5 California State University 6527 54.0 Connecticut College 17734 83.5 Pomona College 28418 95.3
The police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
A soft drink bottling company wants to develop a regression model to predict delivery time (in minutes) based on the number of cases delivered. A sample of 16 deliveries was selected. The Excel output for this regression model is given below. (a) State the regression equation. (b) Interpret the meaning of b0 and b1 in this problem. (c) What is the predicted delivery time when the number of cases is 30 , assuming 30 is within the range of number of cases delivered for this problem? (d) At the 0.05 level of significance, is there evidence of a linear relationship between the number of cases delivered and the delivery time? (e) Construct a 95% confidence interval estimate of the population slope β1. Interpret the confidence interval estimate. (f) How useful do you think this regression model is for predicting the delivery times?
Researchers used the simple linear regression model to study the relationship between social media screen time during a week and end-of-week quiz results. As one of the researchers, find the predicted quiz score if a student spends 18.46 hours during the next week using social media. Use the data in the table below to build the estimated regression equation and then use this equation to find the predicted quiz score: Social media weekly time, hours 14.5 3.7 30.4 34.23 2.7 16.8 13.6 4,7 20,6 4.9 Round your answer to 2 decimals. Less I Quiz results, out of 100 76.8 98.45 57.6 45.5 74.78 75.7 93.67 57.8 35.7 94.8
A professor in the School of Business in a university polled a dozen colleagues about the number of professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (y) during the same period. The summary data are provided. Fit a simple linear regression model between x and y by finding out the estimates of intercept and slope. Comment on whether attending more professional meetings would result in publishing more papers. n n n = 12, x = 4, y = 12, X₁Y₁ = 320 i=1 x² = 234, i=1 The estimated regression line is y = 36.4 + (-6.10 )x. (Round to two decimal places as needed.) Comment on whether attending more professional meetings would result in publishing more papers. Let it be unclear that attending more professional meetings affects the number of published papers if the value used to make that determination is between 1 and 1. Because the of the regression equation is it would appear that attending more professional meetings ▼
A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents attendance (in thousands) and ŷ is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line? For each increase in attendance by 1,000, the predicted number of wins increases by 4.9. For each increase in attendance by 1,000, the predicted number of wins increases by 15.2. For each increase in the number of wins by 1, the predicted attendance increases by 4,900. For each increase in the number of wins by 1, the predicted attendance increases by 15,200.
A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. Which statement best describes the meaning of the slope of the regression line? For each increase in distance by 1 yard, the predicted club speed increases by 2 ft/sec. For each increase in distance by 1 yard, the predicted club speed decreases by 106 ft/sec. For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards. For each increase in club speed by 1 ft/sec, the predicted distance decreases by 106 yards.
The annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!
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…
Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x y 11.8 14.2 8.4 11.37.1 9.83.9 72.6 5.92.5 6.12.1 5.70.5 4.2 x= thousands of automatic weaponsy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 2.2 thousand automatic weapons?Answer = . Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.9 thousand automatic weapons?Answer = .Round to 3 decimal places.
A set of n = 25 pairs of scores (X and Y values) produces a regression equation Y = 3X – 2. Findthe predicted Y value for each of the following X scores: 0, 1, 3, -2.

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