Regression Analysis.pptx

Regression Analysis

1. regression analysis

2. Simple Linear Regression Model “Regression Analysis is a study of relationship between a set of independent variables and the dependent variable” The main purpose of regression analysis is to derive an equation which can be used to estimate the unknown value of dependent variable on the basis of the known value of the independent variable Simple Linear Regression Model A linear relationship is one that can be graphed with a straight line Here we use a straight line to predict values of the dependent variable Assumptions underline linear regression For each value of “x”, there is a group of “y” values and these “y” values are normally distributed “Y” values are independent from each other   - Intercept - Slope of the line / Coefficient of the equation  

3. Simple Linear Regression Model Illustration You are considering enrolling into university Your Friend Roshan tells you; “Don’t go to Uni. My brother Hashan has a PhD, and he’s unemployed” “Dinesh never went to school, and he is rich” Does spending more time in school lead to higher wages???? Survey a bunch of people (eg.100 individuals) Make sure the survey is representative of the population What is the best way to present this data??? SCATTER PLOT DIAGRAM

4. Simple Linear Regression Model The best fit line is the line that best represents the general pattern of the sample

5. Simple Linear Regression Model Finding the Best Fit Line using Method of Least Squares Line of Y on X Equation of the line of best fit; Y = a + bx “When the sum of squares of the vertical deviations from this line becomes least we get the best line” When above happens, we get the following equations known as normal equations.   1 2

6. Simple Linear Regression Model Example 01 A production company of yarn has published data concerning the strength of cotton yarn and the length of the cotton fiber that make up the yarn. Results for 10 pieces of yarn are as follow Assume the relationship of yarn strength is a linear function of fiber length, calculate the sample regression line Predict the average strength of yarn made from fibber of length equal to 80 inches Strength of yarn (Pounds) 99 93 99 97 90 96 93 130 118 88 Fiber length (1/100 an inch) 85 82 75 74 76 74 73 96 93 70

7. Simple Linear Regression Model Example 02 In a small firm, the production of items and the cost during the previous 10 months are shown in the table below Find the least square regression line of cost on production and draw the trend line Find the fixed cost of the firm If the production scheduled for the next 2 months are (a) 10,000 units (b) 15,000 units, predict the total cost for the next 2 months Production (Units’000) 10 8 5 4 6 9 10 12 7 11 Cost (Rs.’000) 22 20 16 11 12 19 15 20 13 24

8. Simple Linear Regression Model Alternative Methods to find “a” and “b” The equation for a linear trend line in a time series is, Example 03 Using the information given in example 02, find the regression coefficients using formula  

9. Analysis of Time Series A time series is a set of observations taken at specified times usually at equal intervals The time interval may be an hour, a day, a week, a month, a quarter, or a year depending on the type of variable Mathematically, time series is defined by values of a variable (Y) at times (t) and thus represent by Y = f(t) Examples of time series The annual production of paddy in Sri Lanka over the last 20 years The monthly sales of a departmental store for the last 5 years The daily closing price of a share in the CSE Time series analysis is a statistical method that helps to understand past behavior of variable and therefore to forecast the future

10. Analysis of Time Series Example 03 The following time series shows the total annual net sales of an electric corporation for the years 2010-2018 Draw the scatter diagram for this data Find the trend line using the method of least squares and draw it on the scatter diagram Forecast sales for the year 2019 Example 04 Traffic police in a district is studying the number of traffic deaths in the district resulting from drunk driving for each of the 8 years 2011-2018 Find the linear equation that describes the trend in the number of traffic fatalities in the district resulting from the drunk driving Estimate the no. of traffic fatalities resulting from drunk driving that the district can expect in the year 2020 Year 2011 2012 2013 2014 2015 2016 2017 2018 No. of Deaths 170 190 185 200 180 200 180 190 Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 Net Sales (Rs. Mn) 145 158 164 144 152 201 190 193 196

11. Chapter Summary The regression line is the “line of best fit ” is the slope of the line. A one unit increase in X will lead to a increase in Y is the value of Y when X is equal to zero > 0 means there is a positive relationship between X and Y < 0 means there is a negative relationship between X and Y = 0 means there is no relationship between X and Y The estimated regression can be used to make predictions for Y given X