Question 978523
Let

x = number of years since 1900 (x = 0 represents 1900, x = 1 represents 1901, etc)
y = CPI for a given year x years after 1900


CPI = Consumer Price Index



<table border=1><tr><th>Year</th><th>CPI</th></tr><tr><td>40</td><td>14</td></tr><tr><td>50</td><td>24.1</td></tr><tr><td>60</td><td>29.6</td></tr><tr><td>70</td><td>38.8</td></tr><tr><td>80</td><td>82.4</td></tr><tr><td>90</td><td>130.7</td></tr><tr><td>100</td><td>172.2</td></tr><tr><td>105</td><td>195.3</td></tr><tr><td>108</td><td>215.3</td></tr></table>


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a)


Use a calculator (like a TI83) or excel to find the equation of the regression line.

If you have neither, then use this <a href="http://www.alcula.com/calculators/statistics/linear-regression/">free online calculator</a> and it will get the job done.


The regression line is {{{y=3.096940216896x-141.63877471977}}} (this is approximate)

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b)


Plug in x = 117 (Note: 2017 - 1900 = 117) to find the predicted CPI in 2017


{{{y=3.096940216896x-141.63877471977}}}


{{{y=3.096940216896*117-141.63877471977}}}


{{{y=220.703230657062}}}


{{{y=220.7}}}



I rounded the result to 1 decimal place because all of the other CPI values are shown accurate to 1 decimal place.


The predicted CPI in the year 2017 is <font color="red">220.7</font>

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c)


Plug in {{{y = 300}}} and solve for x


{{{y=3.096940216896x-141.63877471977}}}


{{{300=3.096940216896x-141.63877471977}}}


{{{300+141.63877471977=3.096940216896x}}}


{{{441.63877471977=3.096940216896x}}}


{{{441.63877471977/3.096940216896=x}}}


{{{142.604875712589=x}}}


{{{x=142.604875712589}}}


Round to the nearest whole number to get {{{x = 143}}}


It will take 143 years for the CPI to pass 300. So the CPI will pass 300 in the year 1900+143 = <font color="red">2043</font>