what is the method used to find the equation of the regression line called
Regression Equation: Overview
A regression equation is used in stats to discover out what relationship, if whatsoever, exists between sets of data. For case, if y'all measure out a kid's pinnacle every year you might observe that they grow about 3 inches a year. That trend (growing 3 inches a yr) tin can exist modeled with a regression equation. In fact, virtually things in the real earth (from gas prices to hurricanes) can be modeled with some kind of equation; it allows us to predict future events.
Watch the video for an overview.
What is a Regression Equation?
Can't come across the video? Click here.
A regression line is the "all-time fit" line for your data. You lot basically describe a line that best represents the data points. It'south like an average of where all the points line up. In linear regression, the regression line is a perfectly straight line:
A linear regression line.
The regression line is represented past an equation. In this case, the equation is -2.2923x + 4624.4. That ways that if you graphed the equation -2.2923x + 4624.4, the line would be a rough approximation for your data.
It'due south not very common to have all the information points actually autumn on the regression line. In the above image, the dots are slightly scattered around the line. In this next epitome, the dots fall on the line. The curved shape of this line is as a result of polynomial regression, which fits the points to a polynomial equation.
Polynomial regression results in a curved line.
Regression Lines and Prediction
Regression is useful every bit it allows you to make predictions most data. The first chart above goes from 1995 to 2015. If you lot wanted to predict what would happen in 2020, you could plug it into the equation:
-2.2923(2020)+4626.4 = -4.046.
Having a negative rainfall doesn't brand too much sense, simply yous tin can say that rainfall is going to drib to 0 inches erstwhile before 2020. According to this item regression line, it really is predicted to happen quondam in 2018:
-2.2923(2018)+4626.4 = 0.5386
-2.2923(2019)+4626.4 = -1.7537
What is a Regression Equation used For?
Regression equations can help you effigy out if your information can be fit to an equation. This is extremely useful if you want to make predictions from your data--either future predictions or indications of past beliefs. For example, you lot might want to know what your savings are going to exist worth in the hereafter. Or, you might want to predict how long it can take to recover from an illness.
At that place are several types of regression equations. Some of the more mutual include exponential and uncomplicated linear Regression (to fit the data to an exponential equation or a linear equation). In elementary statistics, the regression equation you lot are almost likely to come beyond is the linear grade.
Computing Linear Regression
Need assistance with a homework question? Bank check out our tutoring page!
There are several ways to detect a regression line, including past manus and with technology, like Excel (encounter below). Finding a regression line is very tedious by hand. The following video illustrates the steps:
Tin't see the video? Click here.
You tin can as well discover a regression line on the TI calculators:
- TI 83 Regression.
- How to perform TI-89 Regression.
The linear regression equation is shown beneath.
Downside of Regression Analysis
In order to brand data fit an equation, you accept to effigy out what general pattern the data fits commencement. The general steps to performing regression include commencement making a scatter plot and then making a guess as to what kind of equation might be the best fit. Then you can select the best regression equation for the job.
The data in this besprinkle plot looks clustered around a directly line, so is suitable for linear regression.
However, as the following image shows, it isn't always completely straightforward to select the advisable regression equation, peculiarly when y'all're dealing with real life data. Sometimes you lot get "noisy" data that doesn't seem to quite fit whatsoever equation. If the bulk of the information looks similar it follows a design, you could omit the outliers. In fact, if y'all ignore outliers, the data looks like it could be modeled by an exponential equation.
.
Regression Equation in Microsoft Excel 2007/2010
1 benefit of using Excel to plot your data is that you can play around with the regression equation until y'all have something that works. You only need to type your data in in one case, then y'all can add and delete every bit many graphs as you wish.
Regression Equation Microsoft Excel: Steps
Example Problem: Find the regression equation for the following information prepare using Microsoft Excel 2007 or 2010:
- x = 1, ii, 3, 4, 5, 6, 7
- y = i, 3, 6, 12, 24, 39, l
Step 1: Type your data into two columns. Place the x-values in column A and your y-values in column B.
Step ii: Highlight the two columns: Click in cell A1 and then drag the cursor to cell B7.
Step 3: Click "Insert," so click "Scatter" and then click "Scatter with only markers."
Step 4: Select any data point on the graph. In other words, select an actual data bespeak — "X" will appear over each point on the graph. Right-click and and so click "Add together trendline.
Step five: Cull a type of regression. The data suggests that this might be an exponential equation, so click the "Exponential" radio button.
Step 6: Click the "Brandish Equation on chart" box and then click "Close." The regression equation for this particular Excel graph is y=8.4643x-14.571.
Tip: If your graph line doesn't look correct, repeat the steps and see if another type of regression (for instance, linear) might fit better.
Check out our Youtube channel for more tips and help for stats!
References
Gonick, 50. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
---------------------------------------------------------------------------
Need help with a homework or test question? With Chegg Written report, you lot tin can get step-by-stride solutions to your questions from an expert in the field. Your kickoff 30 minutes with a Chegg tutor is free!
Comments? Need to post a correction? Please post a comment on our Facebook page .
Source: https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-a-regression-equation/
0 Response to "what is the method used to find the equation of the regression line called"
Postar um comentário