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Why you call regression line as line of fit?
It is called the line of best fit because it tends to satisfy all the possible points in consideration at the same time with minimal variation.
When doing linear regression if the correlation coefficient is positive the slope of the line is negative?
False.
What is the difference between a trend line and a line of best fit?
A trend line is graphed from a linear, exponential, logarithmic or other equation, and trys to fit the sorted data that you have. But it may or may not be correlated. The line of best fit is the trend line that best fits your data, having a high correlation. R closer to 1.
How can you use a scatter plot to find an equation of a trend line?
By finding the line of best fit and using the straight line equation formula.
Does the trend line always pass through every point on a scatter plot?
No. When you draw a best line of fit on the scattered plot, the line would not be straight.
Definition of trend in math terms?
Usually it refers to the straight line regression of a variable against time.
How can you find an equation for a trend line?
There are numerous ways to do this. I think the easiest is to put the data in excel and have excel show the trend line, equation, andcorrelation coefficient. Excel gives you several options to choose for the trend line analysis. The other way is if it is a linear relationship, you can do the linear regression analysis following the steps listed in the related link. If you are not familiar with regression analysis, it may not be easy for you to follow.
Is the line of best fit the same as linear regression?
Linear Regression is a method to generate a "Line of Best fit" yes you can use it, but it depends on the data as to accuracy, standard deviation, etc. there are other types of regression like polynomial regression.
A trend line on a graph is the same as the line of best fit?
No.
A trend line on a graph is always the same as the line of best fit?
No.
How does a linear regression allow us to better estimate trends costs and other factors in complex situations?
You question is how linear regression improves estimates of trends. Generally trends are used to estimate future costs, but they may also be used to compare one product to another. I think first you must define what linear regression is, and what the alternative forecast methods exists. Linear regression does not necessary lead to improved estimates, but it has advantages over other estimation procesures. Linear regression is a mathematical procedure that calculates a "best fit" line through the data. It is called a best fit line because the parameters of the line will minimizes the sum of the squared errors (SSE). The error is the difference between the calculated dependent variable value (usually y values) and actual their value. One can spot data trends and simply draw a line through them, and consider this a good fit of the data. If you are interested in forecasting, there are many methods available. One can use more complex forecasting methods, including time series analysis (ARIMA methods, weighted linear regression, or multivariant regression or stochastic modeling for forecasting. The advantages to linear regression are that a) it will provide a single slope or trend, b) the fit of the data should be unbiased, c) the fit minimizes error and d) it will be consistent. If in your example, the errors from regression from fitting the cost data can be considered random deviations from the trend, then the fitted line will be unbiased. Linear regression is consistent because anyone who calculates the trend from the same dataset will have the same value. Linear regression will be precise but that does not mean that they will be accurate. I hope this answers your question. If not, perhaps you can ask an additional question with more specifics.
A point that is always on the regression line?
(mean x, mean y) is always on the regression line.
Is a line graph the same as a trend graph?
No. Generally speaking, a trend graph has time on the horizontal axis. That is not always the case with line graphs.
Is a trend line on a graph always the same as the line of best fit?
Usually yes.
Why are there two regression lines?
There are two regression lines if there are two variables - one line for the regression of the first variable on the second and another line for the regression of the second variable on the first. If there are n variables you can have n*(n-1) regression lines. With the least squares method, the first of two line focuses on the vertical distance between the points and the regression line whereas the second focuses on the horizontal distances.
Given a linear regression equation of equals 20 - 1.5x where will the point 3 15.5 fall with respect to the regression line?
on the lineGiven a linear regression equation of = 20 - 1.5x, where will the point (3, 15) fall with respect to the regression line?Below the line
A trend equation is a regression equation in which?
A trend equation is a regression equation that models the relationship between a variable and time. It is used to identify and forecast trends in data over time, helping to predict future values based on historical patterns. Trend equations can be linear or nonlinear, depending on the nature of the data being analyzed.
