REGRESSION ANALYSIS: DETECTION, EFFECTS AND REMEDIAL MEASURES OF DEPARTURES ONASSUMPTIONS OF REGRESSION MODELMethod of DetectionDepartures/Violations on AssumptionsEffects of theviolations on theRemedialGraphicalStatisticalMeasuresmodel4. The model fits all but one or a few outlierobservation.5. The error terms are not nomallydistributed.6. There is exact linear relationship or exactcollinearity between the X variables.

The given problem involves writing about the method of detection for the departures from…

ASSUMPTIONS OF REGRESSION MODEL Method of Detection Departures Violations on Assumptions Effects of the violations on the model Remedial Measures Graphical Statistical The model ts al but one or a few outler observation. 6. The error terms are not normally distributed 6. There is exact linear relationship or exact

ASSUMPTIONS OF REGRESSION MODEL Method of Detection Departures Violations on Assumptions Effects of the violations on the model Remedial Measures Graphical Statistical The model ts al but one or a few outler observation. 6. The error terms are not normally distributed 6. There is exact linear relationship or exact

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.
Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
4) Conduct a hypothesis test on H0: slope = 0; Ha: slope positive or negative (your hypothesis from part 2). Using α = 0.05, is there a significant linear relationship between x and y (paste your output to support your answer)? What is the linear model (y = mx + b, fill in the numbers for m and b)? In the context of the problem, what is the interpretation of the slope, m? Select Stat menu option across the top and then select Regression -> Simple Linear Enter your x and y variables Under the hypothesis test section go to Ha slope and specify the direction of the relationship (< or >) Select Compute sodium protein 130 1015 2260 9140 14200 1180 1.5125 1210 2200 4210 5220 0290 2210 0140 2180 0280 0290 190 1180 0140 480 1220 1140 2190 1125 1200 10 3160 5240 5135 045 0280 0140 3170 375 3220 1250 1.5180 0170 1170…
An economist uses the regression model Inflation=f(unemployment) to test the Phillips Curve theory on South African data. A slope of -0.21 is estimated, and the economist wants to do a hypothesis test to check whether the true value is negative. Would it be appropriate to conduct a two-sided test on the slope parameter? What would the appropriate H0 and H1 be? A. Yes, because the theory suggests a negative slope, therefore it is of interest to determine whether the slope coefficient is different from zero. H0=0 and H1≠0. B. Yes, because the only test of interest is whether the slope estimate is equal to zero or not. H0=0 and H1≠0. C. Yes, because the slope could be either negative or positive and the hypothesis test is based on the t distribution which takes negative or positive values. H0=0 and H1≠0. D. No, because the theory suggests a negative slope, therefore it is of interest whether or not the β2 coefficient is negative rather than different from zero. H0=0 and H1<0. E.…
Calculate the simple linear regression to determine if the amount of sleep (y) can be predicted by time spent on homework (x). Graph the relationship and determine, numerically, if there are any outliers. Interpret all results in a paragraph citing the appropriate statistics. Sleep in minutes (Y): 360,400,420,440,540,480,320,440,360,420,420,390,360,480,360,360,480,420,360,480,270,360,420,360,420 Homework in minutes (X): 30,45,60,15,75,120,80,60,100,45,60,50,60,120,60,60,60,60,90,180,165,90,60,60,90
Chicken Chicken sandwiches are often advertisedas a healthier alternative to beef because many are lower in fat. Data from tests on 15 different sand-wiches randomly selected from the website http:// fast-food-nutrition.findthebest.com/d/a/Chicken-Sandwich produced the Calories vs. Fat scatterplot and the regression analysis below. a) Do you think a linear model is appropriate in thissituation?b) Describe the strength of this association.c) Write the equation of the regression line to estimatecalories from the fat content.d) Explain the meaning of the slope.e) Explain the meaning of the y-intercept. f) What does it mean if a certain sandwich has a nega-tive residual?
Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size---- that is, that total time (in minutes) to produce a certain quantity of the product. She has collected data on the total time to produce 30 different orders of various quantities in the file Setup. A)Write out the estimated linear regression equation. ( define the variables first.) B) Interpret the intercept coefficient. C)Interpret the slope coefficient. D) Test for a significant relationship. Use α = 0.05. file Setup Quantity 105 125 135 141 149 171 190 204 206 240 255 277 299 335 371 388 392 400 421 439 439 455 458 480 486 493 506 586 589 665 Total Time 173 188 222 324 249 318 371 185 250 176 396 226 227 368 490 352 429 411 545 442 320 588 484 512 422 404 700 592 457 642
The quality of the orange juice produced by a certain manufacturer is constantly monitored. Data collected on the sweetness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Find and interpret the coefficient of determination, r2, and the coefficient of correlation, r. Find and interpret the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of determination, r2, is enter your response here. Sample variations in the amount of water-soluble pectin explain 100r2% of the sample variation in the sweetness index using the least squares line. B. The coefficient of determination, r2, is enter your…
A student is preparing to take a standardized exam. She was told that she needs to get plenty of sleep the night before the exam. She is interested in the relationship between the number of hours of sleep a student gets before the exam and the score earned on the exam. She collects information from 10 other students who have already taken the exam as shown in the table. Based on the residual plot, is the linear model appropriate? No, there is no clear pattern in the residual plot. Yes, there is no clear pattern in the residual plot. No, the student who got the most sleep had a negative residual. Yes, there are more negative residuals (6) than positive residuals (4).
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.