document.write( "Question 1125291: The following data is associated with the problem:\r
\n" ); document.write( "\n" ); document.write( "Year Population (in millions)
\n" ); document.write( "1950 6.79
\n" ); document.write( "1960 27.81
\n" ); document.write( "1970 45.59
\n" ); document.write( "1980 69.01
\n" ); document.write( "1990 84.39
\n" ); document.write( "2000 110.21\r
\n" ); document.write( "\n" ); document.write( "A: use x=0 for 1950, x=10 for 1960,....
\n" ); document.write( "The linear regression equation that best fits this data in the form y=ax+b is: ______________. Round the constants to the nearest thousandth.\r
\n" ); document.write( "\n" ); document.write( "B: Use your regression equation to predict the population if x=5.15\r
\n" ); document.write( "\n" ); document.write( "c: Approximate in what year the population reaches 38.05 million. \n" ); document.write( "

Algebra.Com's Answer #741721 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "Year Population (in millions)\r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ | $\"y\"$
\n" ); document.write( " $\"1950\"$ | $\"+6.79\"$
\n" ); document.write( " $\"1960\"$ | $\"+27.81\"$
\n" ); document.write( " $\"1970\"$ | $\"+45.59\"$
\n" ); document.write( " $\"1980\"$ | $\"+69.01\"$
\n" ); document.write( " $\"1990\"$ | $\"+84.39\"$
\n" ); document.write( " $\"2000\"$ | $\"+110.21\"$ \r
\n" ); document.write( "\n" ); document.write( "A:
\n" ); document.write( "use $\"x=0+\"$ for $\"1950\"$ , $\"x=10\"$ for $\"1960\"$ ,....
\n" ); document.write( " $\"x\"$ | $\"y\"$
\n" ); document.write( " $\"0\"$ | $\"+6.79\"$
\n" ); document.write( " $\"10\"$ | $\"+27.81\"$
\n" ); document.write( " $\"20\"$ | $\"+45.59\"$
\n" ); document.write( " $\"30\"$ | $\"+69.01\"$
\n" ); document.write( " $\"40\"$ | $\"+84.39\"$
\n" ); document.write( " $\"50\"$ | $\"+110.21\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The linear regression equation that best fits this data in the form $\"y=ax%2Bb\"$ is: \r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%2Bb\"$ use $\"x=0\"$ | $\"+y=6.79\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6.79=a%2A0%2Bb\"$
\n" ); document.write( " $\"b=6.79\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%2Bb\"$ use $\"x=10\"$ | $\"+y=27.81\"$ and $\"b=6.79\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"27.81=10a%2B6.79\"$
\n" ); document.write( " $\"27.81-6.79=10a\"$
\n" ); document.write( " $\"21.02=10a\"$
\n" ); document.write( " $\"a=21.02%2F10\"$
\n" ); document.write( " $\"a=2.102\"$
\n" ); document.write( "
\n" ); document.write( "_____ $\"y=2.102x%2B6.79\"$ _________. Round the constants to the nearest thousandth.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "B: Use your regression equation to predict the population if $\"x=5.15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=2.102%2A5.15%2B6.79\"$
\n" ); document.write( " $\"y=10.8253%2B6.79\"$
\n" ); document.write( " $\"y=17.615\"$
\n" ); document.write( "c: Approximate in what year the population reaches $\"38.05\"$ million. \r
\n" ); document.write( "\n" ); document.write( " $\"38.05=2.102x%2B6.79\"$
\n" ); document.write( " $\"38.05+-6.79++=2.102x\"$
\n" ); document.write( " $\"31.26++=2.102x\"$
\n" ); document.write( " $\"31.26+%2F2.102=x\"$
\n" ); document.write( " $\"x=14.9\"$ ....Approximately\r
\n" ); document.write( "\n" ); document.write( "since $\"x=10\"$ represents year $\"1960\"$ , $\"x=14.9=10%2B4.9\"$ will represent $\"1960%2B4.9=1964.9\"$ year which means in year $\"1964\"$ , and almost $\"11\"$ months which means in November, $\"1964\"$ \r
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