In the following multiple regression equation, what is value of x2 when x1 = 12.5 and ŷ is estimated to be 443? ŷ = 127 + 8x1 + 18x2 X2 =
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.
![In this problem, we are given a multiple regression equation and asked to find the value of \( x_2 \) given specific values for \( x_1 \) and \( \hat{y} \).
The regression equation is:
\[
\hat{y} = 127 + 8x_1 + 18x_2
\]
We need to calculate the value of \( x_2 \) when \( x_1 = 12.5 \) and \( \hat{y} = 443 \).
**Calculation:**
Substitute \( x_1 = 12.5 \) and \( \hat{y} = 443 \) into the equation:
\[
443 = 127 + 8(12.5) + 18x_2
\]
Solve for \( x_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b0530d3-c31a-49f5-8755-a552ab36f2ee%2F45532a9f-8609-4e97-ae18-1f1d5e294056%2Fxjcuc6l_processed.jpeg&w=3840&q=75)
From the information, given that
The multiple linear regression equation is,
Given that the value of x1=12.5 and the predicted value of y is 443.
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