Question

Listed below are amounts of court income and salaries paid to the town justices. all amounts are in thousands of dollars.

Court income 66.0 403.0 1566.0 113.0 270.0 253.0 110.0 156.0 34.0

justice salary 29 46 90 57 44 62 26 27 17

the percent of variations in justice salary that can be explained by court income is, approximately = _ (answer with a percent rounded to the hundreths decimal place)

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Justice Salary
Independent Variable: Court Income
Justice Salary = 31.263776 + 0.039254801 Court Income
Sample size: 9
R (correlation coefficient) = 0.82041619
R-sq = 0.67308272
Estimate of error standard deviation: 13.971241

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	31.263776	5.7740603	≠ 0	7	5.4145219	0.001
Slope	0.039254801	0.010340189	≠ 0	7	3.796333	0.0067

Hence,

Percent of variations in justice salary that can be explained by court income

= R - sq %

= 67.31 %