Question

A marine biologist recorded the number of deaths of specific fish species from the last 10 years due to pollution in a specific area off the Pacific coast. She was curious to see if there was a trend. Identify the best mathematical model with its corresponding R² value and tell whether it is a good model.

Year	1	2	3	4	5	6	7	8	9	10
Deaths	9	8	6	24	19	1	10	15	18	21

A. quadratic model, 0.176

Yes, 0.176 is very close to 0.

B. quadratic model, 0.176

No, 0.176 is a very low R² value.

C. linear model, 0.163

No, 0.163 is a very low R² value.

D. linear model, 0.163

Yes, 0.163 is very close to 0.

Answer 1

data

deaths	year	year^2
9	1	1
8	2	4
6	3	9
24	4	16
19	5	25
1	6	36
10	7	49
15	8	64
18	9	81
21	10	100

linear regression result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.404158042
R Square	0.163343723
Adjusted R Square	0.058761689
Standard Error	7.179727352
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	80.51212121	80.51212121	1.56187173	0.246712981
Residual	8	412.3878788	51.54848485
Total	9	492.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	7.666666667	4.904687513	1.563130505	0.15664924	-3.643563019
year	0.987878788	0.790461966	1.249748667	0.246712981	-0.834929774

quadratic regression result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.419844848
R Square	0.176269696
Adjusted R Square	-0.059081819
Standard Error	7.615929421
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	86.88333333	43.44166667	0.748963507	0.507279896
Residual	7	406.0166667	58.00238095
Total	9	492.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	10.08333333	8.957489994	1.125687368	0.297407108	-11.09776474
year	-0.220454545	3.741025456	-0.058928908	0.954655739	-9.066574065
year^2	0.109848485	0.331440785	0.33142718	0.750023142	-0.673884434

R^2 for linear model = 0.163

for quadratic model = 0.176

quadratic model ,0.176

0.176 is a very low , hence it is not a good model

option B) is correct