Question

Data collected on the depth of the Mississippi River and the water discharge are given in the table:

Depth	Discharge (ft3)
1.59	63
2.90	97
3.10	123
3.31	254
3.31	398
4.27	550
4.55	583
6.67	603
6.79	655
6.82	726

Find r², and interpret the results.

0.81; The least-squares regression line, given by ŷ = −126.08 + 122.67x, is not a good fit for the data.

0.90; The least-squares regression line, given by ŷ = −126.08 + 122.67x, is a good fit for the data.

0.81; The least-squares regression line, given by ŷ = −126.08 + 122.67x, is a good fit to the data.

0.81; The least-squares regression line, given by ŷ = 122.67 − 126.08x, is a good fit to the data.

Answer 1

usig excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.90225
R Square	0.814055
Adjusted R Square	0.790812
Standard Error	115.2695
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	465359.2	465359.2	35.02352	0.000354
Residual	8	106296.4	13287.05
Total	9	571655.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-126.081	96.89085	-1.30127	0.229391	-349.511	97.35
Depth	122.6693	20.72793	5.918067	0.000354	74.8706	170.468

the value of R2 is 0.81 option c is true

0.81; The least-squares regression line, given by ŷ = −126.08 + 122.67x, is a good fit to the data.