1. Hypothesis Testing Example 3: Test the hypothesis that the average content of containers of a particular lubricant is 10 litters if the contents of random sample of 10 containers are: 10.2, 9.7, 10.1, 10.3, 10.1, 9.8,9.9,10.4,10.3,and 9.8 litters use 0.01 level of significant and assume that the distribution of content is normal.

2. Hypothesis Testing Solution: Hypothesis

3. Hypothesis Testing 3.Then the critical region is t 3.25, these t are from table 4. Calculated t:

4. Hypothesis Testing Solution: Calculated t is less than tabulated t then we don’t reject H 0 so that the mean is 10

5. Simple Linear Regression Definition: Given a collection of paired sample data the simple regression equation can be written as: Where:

6. Simple Linear Regression x is the independent variable explanatory variable. b 0 is the y intercept of regression equation. b 1 is the slope of regression equation.

7. Simple Linear Regression The above formula is complicated and we can easiest it as:

8. Simple Linear Regression Example 1: Find the regression equation for yx 21 81 63 45

9. Simple Linear Regression Solution: yxx^2xy 2112 8118 63918 452520 Sum20103648

10. Simple Linear Regression Then Then the regression equation model is:

11. Simple Linear Regression Example 2: Find the regression equation model for the bellow data the hypothesis: yx 0.111.3 0.382.4 0.412.6 0.452.8 0.392.4 0.483 0.614.1

12. Simple Linear Regression Solution: Hypothesis: For b 0 For b1

13. Simple Linear Regression Calculations yxx^2xy 0.111.31.690.143 0.382.45.760.912 0.412.66.761.066 0.452.87.841.26 0.392.45.760.936 0.48391.44 0.614.1 16.8 12.501 Sum2.8318.6 53.6 28.258

14. Simple Linear Regression Calculations Then we reject H0, therefore there is effect of b0 on the regression model.

15. Simple Linear Regression Calculations Then we reject H 0, therefore there is effect of b 1 on the regression model.

16. Simple Linear Regression Using regression model for prediction If we know the value of x we can predict y as: Suppose x= 4.3 then

17. Simple Linear Regression Using regression model for calculate errors From data table when x = 4.1 the y = 0.61 but from model Then the error = 0.61-0.6545 = 0.0445. The best model gives the minimum errors. And so on for each value