Global Research Syndicate
No Result
View All Result
  • Latest News
  • Consumer Research
  • Survey Research
  • Marketing Research
  • Industry Research
  • Data Collection
  • More
    • Data Analysis
    • Market Insights
  • Latest News
  • Consumer Research
  • Survey Research
  • Marketing Research
  • Industry Research
  • Data Collection
  • More
    • Data Analysis
    • Market Insights
No Result
View All Result
globalresearchsyndicate
No Result
View All Result
Home Data Analysis

Calculating a Least Squares Regression Line: Equation, Example, Explanation

globalresearchsyndicate by globalresearchsyndicate
November 24, 2019
in Data Analysis
0
Calculating a Least Squares Regression Line: Equation, Example, Explanation
0
SHARES
0
VIEWS
Share on FacebookShare on Twitter

When calculating least squares regressions by hand, the first step is to find the means of the dependent and independent variables. We do this because of an interesting quirk within linear regression lines – the line will always cross the point where the two means intersect. We can think of this as an anchor point, as we know that the regression line in our test score data will always cross (4.72, 64.45).  

READ ALSO

Bitcoin, Ethereum, Ripple, Polkadot, and Chainlink

EOS, Algorand, YFI Price Analysis: 23 January

The second step is to calculate the difference between each value and the mean value for
both the dependent and the independent variable. In this case this means we subtract 64.45
from each test score and 4.72 from each time data point.  Additionally,
we want to find the product of multiplying these two differences together.

You should notice that as some scores are lower than the mean score, we end up with negative values. By squaring these differences, we end up with a standardized measure of deviation from the mean regardless of whether the values are more or less than the mean. 

Let’s remind ourselves of the equation we need to calculate b. 

The symbol sigma (∑) tells us we need to add all the relevant values together. 

If we do this for the table above, we get the following results:

∑(x-x ̅ ) * (y-y ̅ ) = 611.36

And 

∑(x-x ̅ ) ^2 = 94.18

Slotting in the information from the above table into a calculator allows us to calculate b, which is step one of two to unlock the predictive power of our shiny new model:

The final step is to calculate the intercept, which we can do using the initial regression equation with the values of test score and time spent set as their respective means, along with our newly calculated coefficient.

64.45= a + 6.49*4.72

We can then solve this for a:

64.45 = a + 30.63

a = 64.45 – 30.63

a = 30.18

Now we have all the information needed for our equation and are free to slot in values as we see fit. If we wanted to know the predicted grade of someone who spends 2.35 hours on their essay, all we need to do is swap that in for X. 

y=30.18 + 6.49 * X

y = 30.18 + (6.49 * 2.35)

y = 45.43

Drawing a Least Squares Regression Line by Hand

If we wanted to draw a line of best fit, we could calculate the estimated grade for a series of time values and then connect them with a ruler. As we mentioned before, this line should cross the means of both the time spent on the essay and the mean grade received. 

 

And there we have it! A perfect* predictive model that will make our teachers’ lives a lot easier.

Related Posts

Bitcoin, Ethereum, Ripple, Polkadot, and Chainlink
Data Analysis

Bitcoin, Ethereum, Ripple, Polkadot, and Chainlink

January 23, 2021
EOS, Algorand, YFI Price Analysis: 23 January
Data Analysis

EOS, Algorand, YFI Price Analysis: 23 January

January 23, 2021
Bulls take a brief pause near 1-month old descending trend-line resistance
Data Analysis

Recapturing $1857 is critical for XAU/USD in the FOMC week ahead – Confluence Detector

January 23, 2021
Ripple price regression targets a disappointing $0 by February says, analyst
Data Analysis

XRP bulls need to crack 200-DMA to extend the recovery

January 23, 2021
Curve Dao (CRV) pumps 36% as BTC struggles
Data Analysis

Curve Dao (CRV) pumps 36% as BTC struggles

January 23, 2021
Capped under robust resistance after suffering the sell-off– Confluence Detector
Data Analysis

XAU/USD eyes $1,875 as upside target – Confluence Detector

January 23, 2021
Next Post
Global Indoor Daybeds Market Updated Research Data By (2020-2029) : Alpa Salotti, AR.T.EX SAS, arketipo

Global Indoor Daybeds Market Updated Research Data By (2020-2029) : Alpa Salotti, AR.T.EX SAS, arketipo

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

POPULAR NEWS

‘Vatican Blackout’ Trends on Twitter as Trigger-Happy Users Try to Link It with US Election Fraud

‘Vatican Blackout’ Trends on Twitter as Trigger-Happy Users Try to Link It with US Election Fraud

January 10, 2021
Global Food Authenticity Industry

Fifth Third Bank Partners with Cardtronics to Enhance Brand Visibility in Carolinas through ATM Branding Program

February 4, 2020
Horowitz: Asian-American researcher fired from Michigan State administration for advancing facts about police shootings

Horowitz: Asian-American researcher fired from Michigan State administration for advancing facts about police shootings

July 8, 2020
Digital Learning Market 2020 industry report explores segmented by growth opportunities, emerging-trends, and industry verticals till 2025

Online Brand Protection Software Market report reviews size, share, analysis, trends, growth and forecast 2025

March 6, 2020
Survey finds 40% of fashion brands have not paid suppliers | Apparel Industry News

Survey finds 40% of fashion brands have not paid suppliers | Apparel Industry News

May 29, 2020

EDITOR'S PICK

No Significant Change in XMR Since Hard Fork

No Significant Change in XMR Since Hard Fork

December 2, 2019
Livelihood changes +2:38of affected households under resource scarcity: The Son La hydropower project in Vietnam.

Livelihood changes +2:38of affected households under resource scarcity: The Son La hydropower project in Vietnam.

October 30, 2020
Head to Head Survey: NexTier Oilfield Solutions (NEX) & Its Rivals

Financial Survey: Zai Lab (NASDAQ:ZLAB) versus Adial Pharmaceuticals (NASDAQ:ADIL)

January 27, 2020
WTI trading off monthly highs near $33.00 per barrel

Clings to 200-bar SMA around $40.00 in Asia

October 8, 2020

Categories

  • Consumer Research
  • Data Analysis
  • Data Collection
  • Industry Research
  • Latest News
  • Market Insights
  • Marketing Research
  • Survey Research
  • Uncategorized

Recent Posts

  • Reinforcing honor codes to combat distance misconduct – Opinion
  • Bitcoin, Ethereum, Ripple, Polkadot, and Chainlink
  • Tylosin market SWOT Analysis, Segmentation, Applications & Emerging Audience Till 2027 – KSU
  • Privacy Policy
  • Terms of Use
  • Antispam
  • DMCA
  • Contact Us

Copyright © 2020 Globalresearchsyndicate.com.

No Result
View All Result
  • Latest News
  • Consumer Research
  • Survey Research
  • Marketing Research
  • Industry Research
  • Data Collection
  • More
    • Data Analysis
    • Market Insights

Copyright © 2020 Globalresearchsyndicate.com.

Login to your account below

Forgotten Password?

Fill the forms bellow to register

All fields are required. Log In

Retrieve your password

Please enter your username or email address to reset your password.

Log In