A researcher would like to predici the dependent variable Y fram the two independent variables X, and Xg for a sample of N = 18 subjecis. Use muliple linear regression to calculate the coefficient of multiple determination and Lest thesignificance of the overall regression model. Use a significance level a = 0.01.Y53.242.4 56.67532.262.968.226.970.16330.9 57,45244.2 70.152.93355.967.835.3 54.951.14947.839.5 57.4| 46.945.7| 52.760.557.243.261.140.442 | 45,756.142.2 37.351.8 | 58.953,4 51.942.247.537.14846.86633.8 | 61.732.353.4 57.5F=Pvalue -What is your decision for the hypothesis test?O Reject the null hypothesis, H.:B, = B =0O Fail to reject H,What is your final conclusion?O The evidence supports the claim that one ar more of the regression coefficients is non-zeroO The evidence supports the claim that all of the regression coelfficients are zeroOThere is insufficient evidence to support the claim that at least one of the regression coefficients is non-zeroO There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero

Given: N=18 α=0.01Procedure for multiple linear regression model in excel: Step 1: Enter the data. Step 2: Select the Data tab. Step 3: Select Data analysis. Step 4: Select the Regression. Step 5: Select labels, enter the range of Y, X1, X2. The output is given below From the ANOVA table SSreg=255.7109 SSres=972.6535 From the Regression statistics table R square = 0.208172 From the ANOVA table F=1.971752 p-value(significance F)=0.1737 The decision for the hypothesis test Hypothesis H0:β1=β2=0 H1: At least one of the regression coefficients is non-zero. Decision rule If the p-value is greater than the significance level, there is no evidence to reject the null hypothesis. If the p-value is lesser than the significance level, the hypothesis is rejected. The p-value (0.1737) is greater than the significance (0.01) Thus, there is no evidence to reject the null hypothesis. Decision Fail to reject Ho Conclusion There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero.

Math

Statistics

A researcher would like to predic the dependert variable Y from the two independert variables X, and X, for a sample of N= 18 subjects. Use multiple linear regression to calculate the coelficient of multiple determination and test the significance of the overal regression model. Use a signilficance level a= 0.01. XX 53.2 424 56.6 32.2 | 62.9 75 68.2 269 70.1 30.9 57.4 442 70.1 33 I 55.9 63 52 29 67.8 35.3 549 51.1 39.5 574469 605 45.7 527 57.2 | 43.2 I 61.1 49 478 40.4 42 45.7 56.1 42.2 37.3 422 51.8 5a9 47.5 53.4 51.9 37.1 48 46.8 66 33.8 61.7 32.3 53.4| 57.5 SS SS Pvalue What is your decision for the hypothesis test? O Reject the null hypothesis, H;:ß, = B, = 0 OFail to reject H, What is your final condlusion OThe evidence supports the claim that one or more of the regression coefficieres is non zero OThe evidence supports the claim that all of the regression coelficients are zero OThere is insufficient evidence to support the claim that at least one of the regression coelficients is non ero O There is insulfficient evidence to support the claim that all of the regression coefficienes are equal to zero

A researcher would like to predic the dependert variable Y from the two independert variables X, and X, for a sample of N= 18 subjects. Use multiple linear regression to calculate the coelficient of multiple determination and test the significance of the overal regression model. Use a signilficance level a= 0.01. XX 53.2 424 56.6 32.2 | 62.9 75 68.2 269 70.1 30.9 57.4 442 70.1 33 I 55.9 63 52 29 67.8 35.3 549 51.1 39.5 574469 605 45.7 527 57.2 | 43.2 I 61.1 49 478 40.4 42 45.7 56.1 42.2 37.3 422 51.8 5a9 47.5 53.4 51.9 37.1 48 46.8 66 33.8 61.7 32.3 53.4| 57.5 SS SS Pvalue What is your decision for the hypothesis test? O Reject the null hypothesis, H;:ß, = B, = 0 OFail to reject H, What is your final condlusion OThe evidence supports the claim that one or more of the regression coefficieres is non zero OThe evidence supports the claim that all of the regression coelficients are zero OThere is insufficient evidence to support the claim that at least one of the regression coelficients is non ero O There is insulfficient evidence to support the claim that all of the regression coefficienes are equal to zero

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

A researcher would like to predici the dependent variable Y fram the two independent variables X, and Xg for a sample of N = 18 subjecis. Use muliple linear regression to calculate the coefficient of multiple determination and Lest the
significance of the overall regression model. Use a significance level a = 0.01.
Y
53.2
42.4 56.6
75
32.2
62.9
68.2
26.9
70.1
63
30.9 57,4
52
44.2 70.1
52.9
33
55.9
67.8
35.3 54.9
51.1
49
47.8
39.5 57.4| 46.9
45.7| 52.7
60.5
57.2
43.2
61.1
40.4
42 | 45,7
56.1
42.2 37.3
51.8 | 58.9
53,4 51.9
42.2
47.5
37.1
48
46.8
66
33.8 | 61.7
32.3
53.4 57.5
F=
Pvalue -
What is your decision for the hypothesis test?
O Reject the null hypothesis, H.:B, = B =0
O Fail to reject H,
What is your final conclusion?
O The evidence supports the claim that one ar more of the regression coefficients is non-zero
O The evidence supports the claim that all of the regression coelfficients are zero
OThere is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
O There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero

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