Question

Plot Nutrients added # of species 36 36 32 34 30 20 23 21 16 10

Answer 1

SOlution-

(A) Explanatory variable is nutrients added

Response variable is species

Scatter plot of the data is obtained as-

Scatter Plot 40 35 30 25 20 15 10 0 0 0.5 1 15 22.533.544.5

Lookin above, we can expect a negative relationship between the two variables.

(B) After running regression anlaysis in the excel, regression output is-

SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations 0.732105551 0.535978538 0.477975855 5.336058185 10 ANOVA MS Significance F Regression Residual Total 263.1118644 263.1119 9.240582 0.016067379 227.7881356 28.47352 9 490.9 Intercept X Variable 1 Coefficients Standard Error tstat P-value Lower 95% Uper 95% 34.11016949 2.599312938 13.12276 1.08E-06 28.11614311 40.10419588 -3.338983051 1.098410195 3.03983 0.016067 -5.871921502 -0.8060446

Value of R² = 0.5359 So, 53.59% of the total variation in the dependent variable ( species ) is explained by the model.

(C) Testing the hypothesis in the question-

p-value from the above anova table = 0.01607

This is less than 0.05, so null hypothesis is rejected at 5% level of significance and we can conclude that there is a relationship between the two variables.

Thanks!