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.

Hypothesis Testing Solution: Hypothesis

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

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

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

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.

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

Simple Linear Regression Example 1: Find the regression equation for yx

Simple Linear Regression Solution: yxx^2xy Sum

Simple Linear Regression Then Then the regression equation model is:

Simple Linear Regression Example 2: Find the regression equation model for the bellow data the hypothesis: yx

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

Simple Linear Regression Calculations yxx^2xy Sum

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

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

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

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 = = The best model gives the minimum errors. And so on for each value