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Finance allah shmoop what is regression analysis Regression and elses

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no it's not a therapy session in which your psychiatrist

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tries to figure out why you've gone back to using

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passive fires It's simply this the process by which a

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siri's have different independent variables are compay haired to a

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dependent variable to see which might have the greatest effect

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on the value of the dependent variable All right Well

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okay That's The theory of it anyway But what about

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some practical examples Well what are these graphs And what

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do they tell us Well let's take pete the pizza

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joint guy How does he know what's bringing in customers

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Is it his new burrito pizza or the virtual skee

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ball machines he put in the back Well we can

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use some math here to find an equation Usually a

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linear one Linear regression Very fine Mathematic sport That best

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matches the pattern in the data Then we can see

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how close the points are to that line and that

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you know will solve our burrito pizza Steve all conundrum

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and help pete manage his business better Well the closer

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that data points are to the line the more likely

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there's some kind of link between the independent and dependent

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variables well it doesn't mean one variable causes another It

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just means they're linked somehow Like what about the link

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between ice cream sales and drownings Death that's a morbid

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connection but see how cloaks the data points are to

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that special line So yeah there's absolutely some meaningful link

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between ice cream sales and drownings deaths greater ice cream

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sales on a given day is always linked to mohr

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drowning deaths on that day Why what's the linking factor

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Flavor of ice cream of the amount of sugar in

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the ice cream Too much in ice cream fat and

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crap and stuff accessibility to public swimming pools Well clearly

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ice cream isn't some insidious killer drowning people who get

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in the water without waiting the records that you know

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one hour But there is a link between those two

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variables Think about it As it turns out hire isis

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scream sales happen on hotter days so heat or sunshine

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is the linking factor Mohr people go swimming on hotter

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days when more people swim while they're going to be

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more drowning possibilities anyway so i scream sales in drowning

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Deaths are linked but ice cream sales don't cause drowning

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death Got it No causal link there Similarly check out

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how the points in this graph are not really close

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to the line at all There's no link between your

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shoe size and your g p a you know unless

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you buy huge shoes build a mini computer that fits

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in the extra space in your shoes and use that

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to help you you know cheat Don't do that by

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the way Always cite shmoop anyway back to pete the

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owner of zaza pizza Pete almost has more customers lately

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than he can handle while the lightning is striking Pete

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wants to find a way Teo you know bottle it

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The thing is he's made to significant changes to his

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restaurant and he's not sure which one is more responsible

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for the influx of people tossing money of him Is

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it the virtual skee ball machines Or is it his

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new burrito pizza Is there in fact any link at

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all Well it could be both that are responsible but

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that's beyond pete skill and this course to determine he

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can only compare one at a time to the increased

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Revenue so pete picks different days and plots the number

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of burrito pizza orders against the total money made that

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day Notice how the data points seem closely to follow

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an imaginary line there fromthe lower left to the upper

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right In general we can see that low burrito pizza

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order numbers are paired with lower daily revenues Also hi

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burrito pizza orders are paired with higher daily revenues high

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against high low against low will the closer the points

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are too that imaginary line the more likely it is

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that the independent variable in this case burrito pizza sales

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is at least related in some meaningful way to the

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dependent variable like it's the pendant on sales of total

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daily revenue under our tea i eighty for their or

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phone or computer or whatever you're using first week pop

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up our data into the list by pressing the stat

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button Then enter we put in the ex data in

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list one there l won and the y data enlist

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to l two Now we press the second key and

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the mod key to get out of that menu If

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we don't get out of that menu well we're just

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begging to screw the pooch here so get out Get

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out now we bash stat move over to the cal

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commend you and choose option for which is lean wreg

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a x plus be all right That's in texas shorthand

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for linear regression Yeah on the menu it brings up

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moved down to calculator and then press enter if you're

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cal doesn't show the r squared and our values Well

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you need to hit youtube in search for how to

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turn on stat diagnostics t i eighty four there's a

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bunch of important info in the results that we need

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to check out most importantly for pete's sake is the

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value of our the closer that our value is toe

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one or negative one The closer the points are two

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best fit that possible line Well the closer they are

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value is toe one for graphs with positive slopes or

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negative one for graphs with negative slope the stronger the

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link between the independent independent variables there right That link

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is called a correlation right They correlate it doesn't mean

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higher daily revenues are absolutely caused by burrito pizza lovers

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but it does suggest there somehow correlated and that correlation

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is strong anyway The a and b values that you

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see on the display happen to be the slope And

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why intercept of the equation in the best possible line

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pete can use these to predict daily revenues if he

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knows the number of burrito pizza sails in a day

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But that's a different video Pete still needs to know

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if virtual skee ball is so exciting that it might

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be more responsible for daily revenue jumps He also plotted

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the number of times virtual skee ball was played in

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a day versus those same daily revenue figures Well guess

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what The points look like a cloud instead of having

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any obvious linear pattern Well if we pop that data

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into the cal can run the same linear regression process

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again we get a very different our value We can

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also just see that the points aren't that close to

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the line that our value is not close toe one

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at all In fact it's cozying up to zero like

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it's Ah you know frat boy and zero is well

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every girl within a forty meter radius when they are

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value is sniffing around zero like that Well it means

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there's some kind of very weak correlation between the independent

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and deep and it variables We can't stress enough that

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this is in proof of any kind of cause no

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matter how weak between the two variables just that some

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kind of correlation exists and that it's weak pete has

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some evidence that the increase daily revenue is almost all

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about the burrito pizza and only a tiny bit due

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to the virtual skee ball crowd But this is a

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big but pete does not have proof they are Value

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just suggests that there's some kind of link between the

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two variables Not that a change in one variable causes

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a change in the other Still with that significant of

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a difference in our values pete is pretty safe in

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thinking burrito pizza is probably more important in driving higher

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revenues than virtual skee ball Pete used a regression analysis

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on the two different variables he thought might influence his

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bank account the most any decisions he makes killing forward

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should probably be menu focused as opposed to you know

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attraction focused and still he can't forget the virtual skee

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ball entirely It is probably a teeny bit responsible for

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the increased mullah in pete's case the correlation between the

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variables was positive which means that as burrito pizza sales

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or virtual skee ball plays increase well so does daily

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revenue there also negative correlations here is well where as

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one variable increases the other variable decreases Case in point

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carla's customs right next to pete's place carla has customs

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takes broken down golf carts and file suits them up

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They recently made three distinct changes to their builds and

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have noticed a huge decrease in the time it takes

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one of their cards to complete the forty r dash

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will car lot I wanted to figure out which change

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might have been the most responsible for the decreased time's

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Carlota plotted forty yard dash times versus the size of

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the rims that these things right here they're diameter and

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got an r value of negative point one seven nine

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when she ran a linear regression of the data then

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forty yard dash times versus the cylinder diameter there and

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got in our value of negative point six to eight

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when she ran a linear regression of that data then

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the forty yard dash times versus the nitrous oxide concentration

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Is what she ran and she got in our value

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of negative point nine four eight when she ran a

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linear regression of the data Well guess what The simple

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fact here all three plots have some kind of linear

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relationship It does mean that there's some kind of correlation

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between each of these three variables rim size cylinder diameter

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and nitrous oxide concentration you know in the forty yard

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dash time of the golf carts with her mostly electric

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But we won't get technicals here since all the grafts

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have negative slopes and the correlation with nitrous oxide is

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the close to the values to negative one The nitrous

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oxide concentration has the strongest correlation to decrease forty yard

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dash times like it's bad for speed reduced nitrous oxide

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in your golf cart it's important to remember that carlotta

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can't say that the nitrous oxide concentration is the direct

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cause of the faster times All she knows is that

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there's a link or a correlation between them Still with

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further experimentation carlota could establish a causal relationship Carlotta explored

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the relationship between three different variables and their possible effect

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on the time to run the forty yard dash using

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regression analysis She determined all three variables had some kind

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of negative correlation of the times To run the course

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as the nitrous concentration or the rim sides or the

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cylinder diameter increased well the forty yard dash times decreased

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Clearly the nitrous concentration had the strongest correlation Carla should

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probably focus on that concentration for the greatest decrease in

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times She knows she can't ignore the rim size nor

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can she ignore the cylinder diameter as they all contribute

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Toe overall Golf cart forty r dash speed times Right

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regression analysis will never tell us which variable is the

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actual cause It just kind of gives us it's along

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the way it's best to make decisions informed by all

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the variables that are correlated to the dependent variable And

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as kelly clarkson famously saying you know this independent variable 00:10:13.231 --> [endTime] something like that miss independent variable

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