A Statistical Analysis Example of A Full Functional Utilization of An Engineering Calculator

1. A Statistical Analysis Example of A Full Functional Utilization of An Engineering Calculator Li-Fei Huang (lhuang@mcu.edu.tw) Dept. of App. Statistics & Info. Sci. Ming Chuan University, TAIWAN

2. Outline • Introduction • Steps of simple linear regression analysis • Commands for programming • Regression test program • Execution result • Conclusions • References

3. Introduction • The functions and commands of statistical software which is installed in the computer are quite COMPLICATED. • The engineering calculator is EASIER to manipulate and CHEAPER to possess. Today even the PROGRAMMING can be done. • This paper will use CASIO fx-7400G PLUS to do the simple linear regression analysis.

4. CASIO fx-7400G PLUS • The slope, the intercept and the coefficient of correlation are shown directly. • There are NO further results about hypothesis testing. • Lots of basic statistics such as can be extracted from the memory of the calculator to create the program about hypothesis testing.

5. Simple linear regression (Step 1) • The sum of squares for X: • The slope for the regression line: The intercept for the regression line:

6. Simple linear regression (Step 2) • The sum of squares for regression: • The sum of squares for Y or the sum of squares for total: • The sum of squares for error: • The mean squares for error: • The regression F test value:

7. Simple linear regression (Step 3) • The coefficient of determination: • The coefficient of correlation: if X and Y are positively correlated, if X and Y are negatively correlated.

8. Simple linear regression (Step 4) • The t tests for the slope and the intercept: • The confidence interval and the prediction interval for a given value of X:

9. Commands for programming • Parts of commands from CASIO fx-7400G PLUS manual:

10. Regression test program (Step1)

11. Regression test program (Step2)

12. Regression test program (Step3)

13. Regression test program (Step4) • The t tests for the slope and the intercept:

14. Regression test program (Step4) • The SE parts of the confidence interval and the prediction interval for a given value of X:

15. Execution result • One data set in the book of Berenson, Levine, & Krehbiel

16. Execution result (Step 2)

17. Execution result (Step 3)

18. Execution result (Step 4)

19. Conclusion 1 • This particular calculator can produce some built in graphs such as histogram, bar chart, pie chart, line chart, box-and-whisker plot, standard normal probability density function, linear regression line, quadratic regression line, log regression line, exponential regression line and power regression line.

20. Conclusion 2 • Using List 4 in previous example, residual plots can be produced to check whether this data set is suitable for regression analysis or not.

21. Conclusion 3 • Using basic statistics, the following tests besides the regression test can also be fulfilled: z test, one-sample t test, two-sample t test, paired t test, chi-square test for single variance and F test for two variances.

22. Conclusion 4 • Using the built in permutation and combination functions, the probability mass function and cumulative mass function for the following discrete probability distributions can be found: binomial distribution, hyper-geometric distribution, geometric distribution, Poisson distribution and negative binomial distribution.

23. Conclusion 5 • The built in list function can help doing many other analyses such as one way ANOVA, randomized block design, chi-square test for K╳1 table, chi-square test for R╳C table, Wilcoxon rank sum test, etc. • Generally speaking, this particular engineering calculator can accomplish lots of interesting statistical analyses if it’s fully utilized.

24. References • CASIO fx-7400G PLUS manual. • Berenson, Levine, & Krehbiel. Basic Business Statistics—Concepts and applications. Pearson International (Edition 11).

25. The End • Thank you for your watching!