The data in the table show home values (in $MILLIONS) and taxes (in MILLIONS) on

Question

The data in the table show home values (in $MILLIONS) and taxes (in MILLIONS) on those homes

HOME VALUE ($M) 0.6,0.75 ,1.0,1.5,2.0, 2.5,3.0

TAXES ($M) 0.03, 0.09, 0.20, 0.44, 0.69, 1.04, and 1.35

(a) Which is the INDEPENDENT variable (X) and which is the DEPENDENT variable (Y) ?

(b) DRAW a SCATTER PLOT OF THESE TWO VARIABLES (X VS Y) & DOES IT SHOW A RELATIONSHIP VISUALLY ?

(c) Calculate the regression line (least squares line) and fill in the “a” and “b” in the equation: Y-hat = a +b*X

(d) Calculate the CORRELATION COEFFICIENT and DETERMINE if it is SIGNIFICANT

(e) Using your regression equation what does it estimate the taxes to be on a $1 million and the $2.5 million home? AND, what would be the predicted taxes on a home with NO VALUE (e.g., severe water damage). How do these regression equation taxes compare to the actual ones in the Table do you feel?

(f) Interpret the SLOPE of this least squares line.

Explanation / Answer

X HOME VALUE ($M) 0.6 0.75 1 1.5 2 2.5 3 Y TAXES ($M) 0.03 0.09 0.2 0.44 0.69 1.04 1.35 a) Independent variable is Home value as taxes are dependent on home value Dependent variable is taxes b) Scatter plot shows a linear positive relationship c) Y = 0.5477*X - 0.3395 Taxes ($M) = 0.5477*Homevalue ($M) - 0.3395 d) Correlation coeff 0.996545 Reg Line Actual e) Taxes on home value of from reg equ 1 M 0.2082 0.2 2.5 M 1.02975 1.04 They are very close to actual f) The slope is positive with value of 0.5477 This shows that for 1 unit change in value of home value there is a change of 0.5477 unit in the taxes

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