Recall that R² is the multiple coefficient of determination and is an indication of the goodness of fit for an estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and SST is the total sum of squares. SSR R2 = SST We are given that SST = 1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result to three decimal places. SSR R2 SST 1,778

Recall that R² is the multiple coefficient of determination and is an indication of the goodness of fit for an estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and SST is the total sum of squares. SSR R2 = SST We are given that SST = 1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result to three decimal places. SSR R2 SST 1,778

MATLAB: An Introduction with Applications

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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

100%

The following estimated regression equation based on 30 observations was presented.
ý = 17.6 + 3.8x, – 2.3x2 + 7.6x3 + 2.7x4
The values of SST and SSR are 1,808 and 1,778, respectively.
(a) Compute R2.
(b) Compute R,.
a
(c) Comment on the goodness of fit.
Step 1
(a) Compute R?.
Recall that R is the multiple coefficient of determination and is an indication of the goodness of fit for an
estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable
that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take
on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and
SST is the total sum of squares.
SSR
R2 .
SST
1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result
We are given that SST =
to three decimal places.
%3D
SSR
R2
%3D
SST
1,778
%D

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