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data: https://www.limes.one/Content/DataFiles/Brains.txt In what follows use any of the following tests/procedures: Regression, confidence intervals, one-sided t-test,...

data: https://www.limes.one/Content/DataFiles/Brains.txt

In what follows use any of the following tests/procedures: Regression, confidence intervals, one-sided t-test, or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval

Open Brain data. SETUP: Common sense dictates that a person’s IQ and Weight should not be related. However, one never knows until one examines the data. Given the data your job is to check if the common sense assumption is reasonable or maybe it is not.

13. What test/procedure did you perform?

  • a. One-sided t-test
  • b. Two-sided t-test
  • c. Regression
  • d. ​​Confidence interval

14. What is the P-value/margin of error?

  • a. 1.99942E-07
  • b. 0.990977927
  • c. 6.72998E-05
  • d. 0.0001346
  • e. ​​None of these

15. Statistical interpretation

  • a. Since P-value is very small we can confirm the common sense assumption that IQ and Weight are not related.
  • b. Since P-value is large we cannot claim that averages are different .
  • c. Since P-value is large we cannot claim that IQ and Weight are related.
  • d. None of these

16. Conclusion

  • a. I have no statistical evidence to claim that IQ and Weight are related.
  • b. I am confident that IQ and Weight are related.
  • c. I am confident that IQ and Weight are not related.
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Answer #1

13. We will conduct a regression test to check if there is any linear relationship between IQ and Weight.
Hence, C) Regression is the correct option.

14. Let's run the regression test in Microsoft Excel by going to Data -> Data analysis -> Regression. The test results are:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.002703
R Square 7.3E-06
Adjusted R Square -0.05555
Standard Error 20.5905
Observations 20
ANOVA
df SS MS F Significance F
Regression 1 0.055737 0.055737 0.000131 0.990978
Residual 18 7631.436 423.9687
Total 19 7631.491
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 78.21778 36.40676 2.148441 0.045537 1.730027 154.7055 1.730027 154.7055
IQ -0.0041 0.357569 -0.01147 0.990978 -0.75532 0.747124 -0.75532 0.747124

We can see that the p-value of the slope (in bold) is 0.9900978. Hence, option B) is correct.

3. Since the p-value is very large, we cannot claim that the variables weight and IQ are related to each other. Hence, C) is correct.

16. Conclusion: a) We do not have enough evidence to say that weight and IQ are related. A) is correct.

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