Question

The following data is provided from the 2015 local housing selling prices and annual taxes.

Is there a linear correlation between the housing selling price and annual taxes? Use mathematical justification and statistical analysis.

Answer 1

When it says mathematical justification and statistical analysis, what does it mean? There are several ways to approach this problem using mathematical justification. Is it a full statistical report?

Answer 2

I guess it is

Answer 3

Okay, I'll break it down for you but I'm not doing the full report for you.

Answer 4

thats fine

Answer 5

Approaches:
A. Graphing it and visually checking for linear association and correlation coefficient, r
B. r^2-value
C. Residuals
D. Linear Regression T test

Are you familiar with these terms? You'll have to include all of them as it's a statistical report.

Answer 6

yea i think I know them

Answer 7

A. Correlation Coefficient:
-enter the sale price values in L1 and respective taxes in L2 on your graphing calculator
-using your graphing calculator, find the Linear Regression (I have a ti 84 so there's an option available for it.)
-You'll get a linear regression β0 and β1 value and using that you can make your linear regression.
-Look at the r value and if the absolute value of it is near 1, then it is a strong correlation, if it is around 0.7 it is moderately high, if it is less than 0.3 it is a weak correlation
B. r^2-value
-You'll get an r^2 value as well.
r^2% of the variance of the y-variable, annual taxes, can be explained by the LSRSL of the x-variable, housing sales. so if it's high, the linear regression is accurate.
C. Residuals
-You can make a residual plot using whichever graphing calculator you have. Observe if there is an equal distribution of points above the residual line and below the residual line. If so, the linear regression is accurate. If not, then the linear regression is not representative of the data.
D. this is the most important and the question is most likely looking for it here.

You will have to complete a linear regression T test, and in your statistical report you must remember to list all the parameters, conditions, calculations, and conclusions.

Answer 8

thx