The following estimated regression equation based on 10 observations was presented.ŷ = 23.1170 + 0.5101x, + 0.4920x2%3DHere, SST = 6,722.125, SSR = 6,224.375,0.0816, and= 0.0569.%3Dzas(a) Compute MSR and MSE. (Round your answers to three decimal places.)MSR =MSE =(b) Compute F and perform the appropriate F test. Use a = 0.05.State the null and alternative hypotheses.Но: В + 0 and B, + 0H: One or more of the parameters is equal to zero.Ho: B1 > B2Hg: Bq s BzHo: B1 = B2 = 0: One or more of the parameters is not equal to zero.%DHo: B1 < B2Ho: B1 + 0 and ß, = 0%3DHa: B1= 0 and B, # 0Find the value of the test statistic. (Round your answer to two decimal places.)F =Find the p-value. (Round your answer to three decimal places.)p-value =State your conclusion.Reject Ho. There is sufficient evidence to conclude that the overall model is significant.Do not reject Ho. There is sufficient evidence to conclude that the overall model is significant.Reject Ho. There is insufficient evidence to conclude that the overall model is significant.Do not reject Ho. There is insufficient evidence to conclude that the overall model is significant. (c) Perform at test for the significance of B,. Use a = 0.05.State the null and alternative hypotheses.Ho: B1 > 0Ho: B1 = 0Ha: B1 + 0Ho: B1= 0Ha: B1 > 0Ho: B, + 0H3: B1 = 0Hoi B1H3: B1 2 0< 0Find the value of the test statistic. (Round your answer to two decimal places.)t =Find the p-value. (Round your answer to three decimal places.)p-value%DState your conclusion.Do not reject Ho. There is sufficient evidence to conclude that B, is significant.Reject Ho.There is sufficient evidence to conclude that ß, is significant.Reject Ho. There is insufficient evidence to conclude that ß, is significant.Do not reject Ho: There is insufficient evidence to conclude that B, is significant.(d) Perform at test for the significance of B,. Use a = 0.05.State the null and alternative hypotheses.Ho: B2 > 0Ha: B2s 0Ho: B2 = 0Ha: B2 > 0

Given information: The sample size is n = 10. The given values are as follows:

Answered: The following estimated regression…

The following estimated regression equation based on 10 observations was presented. ŷ = 23.1170 + 0.5101x, + 0.4920x2 6,224.375, Sby = 0.0569. Here, SST = 6,722.125, SSR = = 0.0816, and

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

The following estimated regression equation based on 10 observations was presented.
ŷ = 23.1170 + 0.5101x, + 0.4920x2
%3D
Here, SST = 6,722.125, SSR = 6,224.375,
0.0816, and
= 0.0569.
%3D
zas
(a) Compute MSR and MSE. (Round your answers to three decimal places.)
MSR =
MSE =
(b) Compute F and perform the appropriate F test. Use a = 0.05.
State the null and alternative hypotheses.
Но: В + 0 and B, + 0
H: One or more of the parameters is equal to zero.
Ho: B1 > B2
Hg: Bq s Bz
Ho: B1 = B2 = 0
: One or more of the parameters is not equal to zero.
%D
Ho: B1 < B2
Ho: B1 + 0 and ß, = 0
%3D
Ha: B1
= 0 and B, # 0
Find the value of the test statistic. (Round your answer to two decimal places.)
F =
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Reject Ho. There is sufficient evidence to conclude that the overall model is significant.
Do not reject Ho. There is sufficient evidence to conclude that the overall model is significant.
Reject Ho. There is insufficient evidence to conclude that the overall model is significant.
Do not reject Ho. There is insufficient evidence to conclude that the overall model is significant.

(c) Perform at test for the significance of B,. Use a = 0.05.
State the null and alternative hypotheses.
Ho: B1 > 0
Ho: B1 = 0
Ha: B1 + 0
Ho: B1
= 0
Ha: B1 > 0
Ho: B, + 0
H3: B1 = 0
Hoi B1
H3: B1 2 0
< 0
Find the value of the test statistic. (Round your answer to two decimal places.)
t =
Find the p-value. (Round your answer to three decimal places.)
p-value
%D
State your conclusion.
Do not reject Ho. There is sufficient evidence to conclude that B, is significant.
Reject Ho.
There is sufficient evidence to conclude that ß, is significant.
Reject Ho. There is insufficient evidence to conclude that ß, is significant.
Do not reject Ho: There is insufficient evidence to conclude that B, is significant.
(d) Perform at test for the significance of B,. Use a = 0.05.
State the null and alternative hypotheses.
Ho: B2 > 0
Ha: B2s 0
Ho: B2 = 0
Ha: B2 > 0

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