Use linear regression to find the equation for the linear function that best fits this data. Round bot numbers to two decimal places. Write your final answer in a form of an equation y = mx + b 1 2 3 4 y 95 126 146 167 197 213
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.
![### Linear Regression Analysis
**Objective:**
To find the equation for the linear function that best fits the given data using linear regression analysis. Round both numbers to two decimal places. Write your final answer in the form of the equation \( y = mx + b \).
**Data:**
The given data points are as follows:
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
y & 95 & 126 & 146 & 167 & 197 & 213 \\
\hline
\end{array}
\]
**Steps to Perform Linear Regression:**
1. **Calculate the means of x and y:**
\[
\bar{x} = \frac{\sum{x}}{n}, \quad \bar{y} = \frac{\sum{y}}{n}
\]
2. **Calculate the slope (m):**
\[
m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}
\]
3. **Calculate the y-intercept (b):**
\[
b = \bar{y} - m\bar{x}
\]
4. **Construct the linear equation:**
\[
y = mx + b
\]
**Explanation of Results:**
After performing the calculations, you will obtain the slope (m) and the y-intercept (b), which you will use to form the final linear equation representing the relationship between x and y.
**Instructions:**
- Ensure to round both \( m \) and \( b \) to two decimal places.
- Substitute the calculated values of \( m \) and \( b \) into the linear equation format \( y = mx + b \).
**Example Solution:**
Suppose, upon performing the calculations, you find:
\[
m = 23.40, \quad b = 75.50
\]
Then, the final linear equation would be:
\[
y = 23.40x + 75.50
\]
Make sure to perform the calculations accurately and report your final answer in the required format.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcebbde0b-56df-456f-b45f-057baf1d3a0f%2F5cf8257a-913f-447e-8637-a9b9e3ed0e90%2Fu2qwecl_processed.png&w=3840&q=75)
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