What does the best estimate mean after doing the liner regression equation

You best approximation of one variable given the value of the other variable.

so would a score of 64.094 be an best estimate

Since I do not have access to your data, I cannot confirm or deny your statement.

here's my data

Student Neatness Rating Achievement Test Grade
1 18 60
2 24 58
3 14 70
4 19 58
5 20 66
6 23 68
7 20 65
8 22 68
9 15 56
10 21 62
11 10 55
12 30 75
13 13 50
14 9 65
15 22 64

In linear regression, the "best estimate" refers to the predicted value of the dependent variable (also known as the response variable) based on the values of the independent variable(s) (also known as the predictor variable(s)) using the linear regression equation.

To understand how to obtain the best estimate in linear regression, you need to follow these steps:

1. Gather and prepare the data: Collect a set of data that consists of paired values of the independent and dependent variables. Ensure that the data is clean and free from any errors or outliers.

2. Construct the linear regression model: Use mathematical techniques to create a linear regression model that represents the relationship between the independent and dependent variables. This model takes the form of a linear equation: y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

3. Estimate the coefficients of the model: Utilize methods like the least squares technique to estimate the values of the coefficients (slope and y-intercept) that minimize the sum of the squared differences between the observed dependent variable values and the predicted values based on the linear regression model.

4. Apply the linear regression equation: Once you have estimated the coefficients, plug in the values of the independent variable(s) into the linear regression equation to obtain the predicted values of the dependent variable. These predicted values are considered the "best estimates" of the dependent variable based on the given data and the linear regression model.

It's important to note that the best estimate is not always exact and may contain some level of error, as linear regression attempts to find the best fit line that minimizes the overall discrepancy between the predicted and observed values.