Question

In: Statistics and Probability

7. Property taxes for an Ontario resident over the years are listed. Year: 2007 2008 2009...

7. Property taxes for an Ontario resident over the years are listed.

Year: 2007 2008 2009 2010 2011 2012

Taxes: $2,900 $3,000 $3,150 $3,300 $3,400 $3,600

a) Draw/sketch a scatter diagram.

b) Calculate the least squares equation.

c) Predict the property tax for the year 2020.

Solutions

Expert Solution

Year (X) Taxes (Y) X * Y X2 Y2
2007 2900 5820300 4028049 8410000
2008 3000 6024000 4032064 9000000
2009 3150 6328350 4036081 9922500
2010 3300 6633000 4040100 10890000
2011 3400 6837400 4044121 11560000
2012 3600 7243200 4048144 12960000
Total 12057 19350 38886250 24228559 62742500

Part a)

Part b)

Equation of regression line is Ŷ = a + bX


b = 138.571
a =( Σ Y - ( b * Σ X) ) / n
a =( 19350 - ( 138.5714 * 12057 ) ) / 6
a = -275234.286
Equation of regression line becomes Ŷ = -275234.2857 + 138.5714 X

Part c)

When X = 2020
Ŷ = -275234.286 + 138.571 X
Ŷ = -275234.286 + ( 138.571 * 2020 )
Ŷ = 4679.13


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