**Section 17.20: Using Multiple Linear Regression**### Objective:Apply multiple linear regression to determine the relationship between variables.### Data Table:The data consists of two independent variables (x₁ and x₂) and one dependent variable (y).| x₁ | 0 | 0 | 1 | 2 | 0 | 1 | 2 | 2 | 1 ||----|---|---|---|---|---|---|---|---|---|| x₂ | 0 | 2 | 2 | 4 | 4 | 6 | 6 | 2 | 1 || y | 14| 21| 11| 12| 23| 23| 14| 6 | 11|### Task:Compute the following:- **Coefficients**: Determine the coefficients that express y as a linear combination of x₁ and x₂.- **Standard Error of the Estimate**: Calculate the standard error to evaluate the accuracy of the predictions.- **Correlation Coefficient**: Find the correlation coefficient to measure the strength of the linear relationship between the variables.### Explanation:Multiple linear regression uses more than one independent variable to predict the outcome of a dependent variable. This exercise involves using statistical methods to derive the necessary coefficients and evaluate predictive accuracy for given data points.

Answered: 17.20 Use multiple linear regression to…

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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2. Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methods.
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10.2.19-T Question Help ▼ Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports Crash Fatality Rate 227 262 363 499 15.4 518 16 15.7 15.4 15 Find the equation of the regression line. (Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.)
3. The following figure shows the Excel output of a least square multiple linear regression for the scores in a test (variable Y) with Hours (X1, the number of hours spent reviewing) and Prep Exam (X2, the number of exams to take) as independent variables. SUMMARY OUTPUT Regression Statisties Multiple R R Square Adjusted R Square 0.857 0.734 0.703 Standard Error 5.366 Observations 20 ANOVA df Significance F 23.46 MS Regression 1350.76 675.38 0.00 Residual 17 489.44 28.79 Total 19 1840.20 Coefficients Standord Error tStat Pvalue 67.67 Lower 95N Upper 95N Intercept 2.82 24.03 0.00 61.73 73.61 hours 5.56 0.90 6,18 0.00 3.66 7.45 prep exams -0.60 0.91 0.66 052 -2.53 133 a. What is the value of r? What is the practical meaning of this value? b. What is the coefficient of Hours? Interpret this value. c. What is the coefficient of Prep Exam? Interpret this value.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = 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 6.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons? Answer = Round to 3 decimal places.
Q2: For the raw data shown in Table below: 1) Find out which of the x₁ or x₂ variables is better correlated to y. 2) Find out the linear regression lines: y₁ = f(x₁) and y2 = f(x₂) depending on the results of 1) above. X1 1 3 4 11 14 X2 1 2 3 12 15 y 1 2 4 9 65 87 99 4 5 сл 7 12 8
8. In an investigation to empirically determine the value of 1, a student measures the circumference and diameter of several circles of varying size and uses Excel to make a linear plot of circumference versus diameter (both in units of meters). A linear regression fit yields the result of: y = 3.1527x - 0.0502, with R2= 0.9967 for the 5 data points plotted. How should this student report the final result? Does the empirical ratio of C/D agree with the accepted value of n?
Q.1/ Use linear regression to fit the following experimental data. 图 2 3 4 5 7 10 y 5.2 7.8 10.7 13 19.3 26.5
4. In a statistical investigation the grade point average (y) and study hour (x) of a group of students are observed as follows: Study hour (x) Grade point (v) 12 17 16 14 11 13 15 3.0 3.2 3.5 4.0 3.8 2.7 3.4 i) Fit a line of y on x and test the significance of regression. ii) Estimate y if x = 17.

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_{$x_{1}$}	$x_{2}$	$y$
0	0	14
0	2	21
1	2	11
2	4	12
0	4	23
1	6	23
2	6	14
2	2	6
1	1	11

17.20 Use multiple linear regression to fit O 2 21 X₁ X₂ y O O 14 1 2 11 2 4 12 0 4 23 1 6 23 2 6 14 2 2 6 1 1 11 Compute the coefficients, the standard error of the estimate, and the correlation coefficient.