Question 1188606
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Part (a)


You could calculate the regression line by hand, but it's tedious busywork in my opinion. Instead, it's better to rely on technology. There are many free options out there that will calculate things like regression lines, correlation coefficients, etc. Many if not all spreadsheet programs can do this, not to mention specialized websites as well. 


After using a spreadsheet program, the regression line I get is
<font color=red>y = 9.77x + 19370.11</font>
Both decimal values are approximate.


x = monthly expenditure on recreation
y = monthly income
both are in dollars


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Part (b)


Using the same spreadsheet program, I get this approximate r value
<font color=red>r = 0.8404</font>


Like with part (a), it's possible to calculate by hand through a formula, but it's preferable to use technology. This is <font color=red>positive correlation</font> because the r value is positive. The regression line has a positive slope which is more evidence we have positive correlation. As x goes up, so does y.

Since r is fairly close to 1, this tells the reader that the linear correlation is fairly strong. 


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Part (c)


Earlier in part (a), we found this regression line
y = 9.77x + 19370.11


The slope of 9.77 tells us that each time x goes up by 1, y roughly increases by 9.77. To put it in more specific context, it means that each time the expenditure x goes up by $1, the monthly income y goes up by about $9.77


The y intercept of 19370.11 indicates that when the expenditure is x = 0, then the monthly income is predicted to be about $19370.11; we can think of this as the initial monthly income so to speak. This is because we can't go any lower than x = 0. Negative x values aren't allowed. 


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Part (d)


Plug x = 5000 into the regression equation and simplify


y = 9.77x + 19370.11
y = 9.77*5000 + 19370.11
y = 48850 + 19370.11
y = <font color=red>68220.11</font>


We estimate that someone spending $5000 per month on recreation will have a monthly income of about <font color=red>$68,220.11</font>
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