Question

The following observations were made about the leaf hopper insect’s body mass versus the altitude at which it was caught in balloon mounted nets. Carry out a model utility test at a significance level of 1.00%. Mass x 10.5 12.6 9.1 11.0 13.0 9.0 16.0 13.0 12.3 12.0 9.0 14.2 Altitude y 1000 900 1200 1000 1100 1300 1200 900 800 1200 1000 800

Answer 1

Run a regression analysis in excel followed by below procedures:

1. Go to data tab --> data analysis --> choose Regression

Get & Transtorm Data Queries & Connections Data Types E2 fic 800 Regression ? Х Input OK Input Y Range: $B$1:$B$13 4 с D Cancel Input X Range: $A$1:$A$13 1 Help Labels Constant is Zero Confidence Level: 95 Output options O Output Range: $E$2] 1 O New Worksheet Ply: A B 1 Mass x Altitude y 2 10.5 1000 3 12.6 900 4 9.1 1200 5 11 1000 6 13 1100 7 9 1300 8 16 1200 9 13 900 10 12.3 800 11 12 1200 12 9 1000 13 14.2 800 14 15 16 17 18 O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

Result:

с D E F G н. J K L M N o P 10.5 SUMMARY OUTPUT بر Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.290 0.084 -0.008 167.599 12 A B 1 Mass x Altitude y 2 1000 12.6 900 4 9.1 1200 5 11 1000 6 13 1100 7 9 1300 8 16 1200 9 13 900 10 12.3 800 11 12 1200 12 9 1000 13 14.2 800 14 15 16 17 18 19 20 21 22 ANOVA df F 0.92 Significance F 0.361 1 MS 25773.49 28089.32 Regression Residual Total SS 25773.49 280893.18 306666.67 10 11 Intercept Mass x Coefficients 1294.95 -22.15 Standard Error 277.36 23.13 t Stat 4.67 -0.96 P-value 0.00 0.36 Lower 95% Upper 95% .ower 95.0%Upper 95.0% 676.94 1912.95 676.94 1912.95 -73.69 29.38 -73.69 29.38

P-value (Significance F) = 0.361 (greater the significance level 1.00%)

If the p-value is NOT less than the significance level (α=0.01)

• Decision: DO NOT REJECT the null hypothesis.
• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is NOT significantly different from zero.