Equation of a line
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Graphing a line in slope intercept form
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Converting to slope-intercept form
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Graphing linear equations
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Linear Equations in Slope Intercept Form
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Graphs Using Slope-Intercept Form
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Word Problem Solving 4
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Equation of a line 1
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Equation of a line 2
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Equation of a Line hairier example
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Equation of a line 3
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Solving for the y-intercept
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Slope intercept form
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Linear Equations in Point Slope Form
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Point slope form
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Linear Equations in Standard Form
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Point-slope and standard form
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Converting between slope-intercept and standard form
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Converting between point-slope and slope-intercept
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Finding the equation of a line
Fitting a Line to Data Fitting a Line to Data
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- In this video I want to give you an example of what it
- means to fit data to a line.
- Instead of doing my traditional video using my
- little pen tablet, I'm going to do it straight on Excel so
- you could see how to do this for yourself, so if you have
- Excel or some other type of a spreadsheet program.
- We're not going to go into the math of it.
- I really just want you to get the conceptual understanding
- of what it means to fit data with line, or do a linear
- regression.
- So here, let's just read the problem.
- The following table shows the median California income--
- remember median is the middle, the middle California income
- --from 1995 to 2002 as reported by
- the U.S. Census Bureau.
- Draw a scatter plot and find the equation.
- What would you expect the median annual income of a
- California family to be in the year 2010?
- What are the meanings of the slope and the y-intercept of
- this problem?
- So the first thing you'd want to do-- I just copied and
- pasted this image --we have to get the data in a form that
- the spreadsheet can understand it.
- So let's make some tables here.
- Let's say years since 1995.
- Let's make that one column.
- Let me make this a little bit wider.
- Then let me put median income.
- This is the median income in California for a family.
- So we start off with 1 year, or 0 years since
- 1995, 0, 1, 2, 3, 4.
- Actually if you want, it'll figure out the trend if you
- just keep going down.
- It'll figure out you're just incrementing by 1.
- Then the income, I'll just copy in these
- numbers right there.
- So that's $53,807, $55,217, $55,209, $55,415 $63,100,
- $63,206, $63,761, and then we have $65,766.
- So I don't need these over here.
- So I'm going to get rid of them.
- I can clear them.
- So let me make sure I have enough entries.
- This is 1, 2, 3, 4, 5, 6, 7, 8, and I have 1, 2, 3, 4, 5,
- 6, 7, 8 entries.
- I want to make sure I got my data right. $53,807, $55,217,
- $55,209, 415, 100, 206, 761, 766.
- OK, there we go.
- Now you're going to find that in Excel this is incredibly
- easy if you know what to click on.
- One, plot this data, create a scatter plot, and then even
- better, create a regression of that data.
- So all you have to do is you select the data.
- Then you go to insert, and I'm going to
- insert a scatter plot.
- Then you can pick the different
- types of scatter plots.
- I just want to plot the data.
- There you go.
- It plotted the data for me.
- There you go.
- If you go by this is the actual income, and this is by
- year since 1995.
- So this is 1995.
- It was $53,807.
- In 1996 it's $55,217.
- So it plotted all the data.
- Now what I want to do is fit a line.
- So this isn't exactly a line.
- But let's see, if we assume that a line can model this
- data well, I'm going to get Excel to fit a line for me.
- So what I can do is I have all of these options up here for
- different ways to fit a line, all of
- these different options.
- I'm going to pick this one here.
- You might not be able to see it.
- It looks like it has a line between dots.
- It also has fx which tells me going to tell me the equation
- of the line.
- So if I click on that, there you go.
- It not only fit, it replotted that same data
- on a different graph.
- Let me make it a little bit bigger.
- No, I don't want to that.
- Let me make it a little bit bigger.
- We can cover up the data now, just because I think we know
- what's going on.
- So let me cover it up right like that.
- So not only did it plot the various data points, it
- actually fit a line to that data and it gave me the
- equation of that line.
- Let me see if I can make this a little bit bigger.
- I'll move it out of the way so you can read it at least.
- So it tells me right here, that the equation for this
- line is y is equal to 1,882.3x plus 52,847.
- So if you remember what we know about slope and
- y-intercept, the y-intercept is 52,847, which is, if you
- use this line as your measure, where this line intersects at
- year 0, or in 1995.
- So if you use this line as a model, in 1995 the line would
- say that you're going to make $52,847.
- The actual data was a little bit off of that.
- It was a little bit higher, $53,807.
- So it was a little bit higher.
- But we're trying to get a line that gets as close as possible
- to all of this data.
- It's actually trying to minimize the distance, the
- square of the distance, between each of these points
- in the line.
- We won't go into the math there.
- But it gave us this nice equation.
- Now we can use this nice equation to predict things.
- If we say that this is a good a model for the data-- let me
- bring this down a little bit --let's try
- to answer our question.
- So we drew a scatter plot-- really Excel did it for us.
- We found the equation right there.
- They say, what would you expect the median annual
- income of a California family to be in the year 2010?
- So here, we can just use the equation they gave us.
- This right here, was 2002.
- So I could write down the year.
- This was the year of 2002.
- So the year 2010 is 8 more years.
- Let me make a little column here.
- So this is the year, 1995, 1996.
- Then Excel will be able to figure out if I select those,
- and I go to this little bottom right square and I scroll
- down, Excel will actually figure out that I want to
- increment by 1 year every time.
- If I say years since 1995, once again I can just continue
- this trend right here.
- So 2010 would be 15 years.
- So we can just apply this equation.
- We could say it's going to be equal to, according to this
- line-- I'm just going to type it in, hopefully you can read
- what I'm saying --1,882.3 times x.
- x here is the year since 1995.
- I could just select this cell, or I could type
- in the number 15.
- That means times this cell, times 15.
- Then plus 52,847, plus that right there.
- Click enter and it predicts $81,081.50.
- So if you just continue this line for another 8 or so
- years, it predicts that the median income in California
- for a family will be $81,000.
- Anyway, hopefully you found that interesting.
- Spreadsheets are very useful tools for manipulating data.
- It'll give you a sense of why linear models are interesting,
- why lines are interesting, and how you can actually use these
- tools to interpret data and maybe even extrapolate some
- type of a prediction.
- This right here, is an extrapolation using this
- linear regression.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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