Descriptive statistics and Regression
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The document presents a detailed overview of descriptive statistics and regression analysis, specifically focusing on various statistical measures such as mean, median, variance, and standard deviation, as well as methods for constructing frequency distribution tables. It also includes practical exercises related to the heights of students and multiple regression analysis concerning income, gas expenses, and trips per day. Key questions guide the analysis and interpretation of statistical results, including hypothesis development and assessment of regression significance.
Descriptive statistics and Regression
- 3. Content • Part – 01 1. Frequency distribution table 2. Arithmetic mean, Median, Mode 3. Mean Deviation 4. Population Variance and Population Standard Deviation. 5. Geometric Mean 6. Sample Variance and Sample Standard Deviation. 7. Coefficient of Variation. • Part – 02 1. Excel output 2. Multicolinearity
- 4. Part – 01 Descriptive statistics
- 5. Height of 20 students of Statistics(ii) class :
- 6. Questions : • Constract a frequency distribution table using both inclusive and exclusive method. • What is the value of data range? • Find out Arithmatic mean. • What is the value of Median? • Find out mode. • Determine the Mean Deviation. • Find out Population Variance and Population Standard Deviation. • Determine the Geometric Mean from the above data. • Find out Sample Variance and Sample Standard Deviation. • What will be the Coefficient of Variation?
- 7. •Constract a frequency distribution table: 2k>n 25 (32) >20 So, Number of classes, K=5 i ≥ = k LH 02.0 5 0.511.5
- 8. INCLUSIVE METHOD (If Interval=3): Classes Frequency Relative Frequency Cumulative Frequency 5.0 -5.2 3 0.15 3 5.3 – 5.5 5 0.25 8 5.6 – 5.8 11 0.55 19 5.9 – 5.11 1 0.05 20 5.12 – 6.1 0 0 20 Total 20
- 9. EXCLUSIVE METHOD (If Interval=3): Classes Frequency Relative Frequency Cumulative Frequency 5.0 to 5.3 3 0.15 3 5.3 to 5.6 5 0.25 8 5.6 to 5.9 11 0.55 19 5.9 to 5.12 1 0.05 20 5.12 to 6.2 0 0 20 Total 20
- 10. •Data Range: Data Range= Highest – Lowest = 5.11-5.0= 0.11 • Arithmetic Mean: µ = = 5.5
- 11. •Arranging data from smallest to Largest: 5.0, 5.0, 5.2, 5.3, 5.5, 5.5, 5.5, 5.5, 5.6, 5.6, 5.6, 5.6, 5.6, 5.7, 5.8, 5.8, 5.8, 5.8, 5.8, 5.11 Median = 𝐻−𝐿 𝐾 = 5.6+5.6 2 = 5.6 Mode Modes are 5.6 and 5.8 (Highest occurrence of 5 times).
- 12. •Mean Deviation: Mean Deviation = 𝑋−𝜇 𝑁 = 4.1 20 = 0.2
- 13. •Population Variance and STD:
- 14. •Geometric mean : Geometric mean, GM = Population Variance, 𝜎2 = 𝑋−𝜇 2 𝑁 = 1.33 20 = 0.0665 Population Standard Deviation, 𝜎 = 𝑋−𝜇 2 𝑁 = 1.33 20 = 0.258 = 5.5
- 15. • Sample Variance and STD: 𝑋 = = 5.5
- 16. • Coefficient of Variation: CV = 𝑆 𝑋 × 100 = 0.264 5.5 × 100 = 4.8%
- 17. Sample Variance, 𝑠2 = (X − 𝑋)2 𝑛−1 = 1.33 20−1 = 0.07 Sample STD, s = (X − 𝑋)2 𝑛−1 = 1.33 20−1 = 0.264
- 19. It is believed that Income per day of a CNG driver is affected by gas expense per day and number of trips per day. Results of the multiple regression equation of Income per day on gas expense per day and number of trips per day are given below.
- 21. • Excel Output:
- 22. • Questions 1) Develop the Hypothesis 2) Find the equation of regression and Interpret. 3) Estimate the relationship among the variables in relative terms. 4) Assess the explanatory power of the independent variables. 5) Assess the significance of the results. 6) Ascertain whether there is a problem of Multicollinearity.