0:00 hello students welcome you all back to my channel hans commerce tutorial i'm harsha marihan again so now we are in the subject business statistics 2. already i have prepared the videos on theoretical distribution in which i have explained we have solved so many problems on binomial distribution poisson distribution and normal distribution already i have prepared the video on uh probability based theorem and one more video i have prepared for permutation and combination so if you have not watched those videos please go to the playlist of my channel select business statistics 2 then you will get all these topics videos now i am going to start the next topic that is regression analysis
0:47 this regression analysis i am going to start now and this regression analysis is not a tough topic just like a probability or binomial distribution price poisson or normal distribution it's a very common topic easily you can understand but many students sorry to say many students think that statistics is a subject only of solving the problem many students have the idea that only solving the problem is enough just we must know how what is the formula how to prepare the table how to i mean substitute the values in the formula how to get the answer but sorry that is not the right way of acquiring the education acquiring the knowledge the purpose of the education is to get the knowledge not simply to pass the examination
1:34 so what i want to say is before solving the problem you must listen the theory what is this what is the subject what is this topic why it is there why it is included in this subject and what is the practical utility of this subject what is the significance of the subject advantage is limitation of this subject then only you should go to the problems right that is the right way of getting the education from my point of view i think so so most of the students will may agree or may not agree but it's a fact so before starting the problem please listen carefully till the end then we'll solve the problems now regression analysis first we are going to discuss about the
2:20 meaning of the term regression analysis see regression literal meaning of the term regression is moving back going back but technically regression analysis is a statistical technique which is concerned with expressing the functional relationship between two or more variables functional relationship between two two or more variables already in business statistics one we have done the topic called correlation that is also related to regression only so in correlation we have seen it's a statistical technique of expressing finding out whether relationship is there or not between two variables two or more variables here regression analysis will give you functional relationship or
3:06 average relationship between two variables there is no cause and effect relationship in correlation analysis but in regression analysis we are going to find we are going to apply the cause and effect relationship between two or more variables so simply regression analysis is a statistical technique of expressing functional relationship between two variables so that we can be able to predict one variable for a given value of the other variable that is the main purpose simple example i'll give you there are many cases where the variables will have some relationship example advertisement and sales the two variables advertisement and sales are related to each other now everybody knows when we give more
3:53 advertisement the sales will may increase sales may increase so by giving less advertisement our sales will be less low so there is some relationship but we cannot be able to predict we cannot be able to predict the sales for a given level for a given amount of advertisement so this regression analysis will solve the problem of predicting predicting one variable for a given value of the other variable that is the regression analysis and it is having much practical utility because it is concerned with prediction prediction forecasting management's main function is planning and planning requires some prediction or forecasting and in that case this regression analysis will be widely used for
4:40 prediction purpose now simple and multiple regression broadly we classify the regression analysis into two types like simple or multiple simple regression is concerned with studying the relationship between two variables only when we consider only two variables then it is called simple regression for example we want to find out the sales and advertisement the relationship between sales and advertisement we are concerned only with two variables it is called simple regression we can say the sales are dependent on advertisement on advertisement similarly demand demand is dependent on price according according to
5:26 economic law there is a law of demand in that case the sales the demand depends on the price higher the price lower will be the demand lower the price higher will be the demand that means both are related to one another so only two variables if we consider that it is called simple simple regression when one when more than two variables are considered at a time it is called multiple regression example the demand does not depend only on price the demand will depend apart from price the income of the people the competition in the market etc so many variables are there so many ways similarly agricultural production and rainfall there is relationship but do
6:14 you think that agricultural production solely depends on rainfall apart from rainfall other factors will also also affect the agricultural production so if we consider more than two variables it will become multiple regression now importance or significance of regression if we compare correlation and regression regression has much more practical utility it is widely used in many cases where we want to predict the value of one variable given the value of the other variable so always two variables will be there one variable is dependent variable other variable is independent variable so we are going to calculate the dependent variable for a given value of the
7:01 independent variable example in case of rainfall and agricultural production the rainfall is independent whereas agricultural production is dependent on rainfall similarly in case of advertisement and sales sales are dependent and advertisement is independent it is in our hands how much we have to give how much we have to spend on advisement we can decide the amount to be spent on advancement but sales will depend on advertisement so always two variables one dependent variable one independent variable will be there in regression analysis the practical utility it's very high because most of the economic problems requires cause and effect relationship
7:48 most of the economic issues or economic cases requires cause and effect relationship so wherever cause and effect relationship is that we apply regression analysis simple example in case of a businessman a businessman has to predict predict about the production consumption profit income investment similarly government the government has to make the prediction or planning for the next future years in that case prediction is required so wherever protection or forecasting is required we can conveniently apply regression analysis to predict the variables next is limitations we don't have only advantages this regression analysis will also
8:34 suffer from some limitations the limitations says that always there will be linear relationship between these two variables between two or more variables but it may not so happen every time there may be non-linear relationship in the same way the functional relationship will be static constant but it may not be true many times the functional relationship or average relationship will change from time to time so some limitations are there of this regression analysis next come differences between correlation and regression there are many similarities as well as differences between correlation and regression in correlation we simply find out whether relationship
9:20 is there or not what is the nature of relationship what is the degree of relationship nature of relationship means we are finding out whether a positive relationship or negative relationship degree of relationship whether it is a strong high degree relationship or low degree relationship but there is no cause and effect relationship in correlation so the utility the advantage or usefulness of this correlation is limited we cannot make any prediction in correlation correlation value simply ranges from minus 1 to plus 1 that's it so only we can be able to get the value and the sign but in case of regression we can be able to predict one variable given the value of the
10:06 other variable so many differences are there between correlation and regression regression is much more important practical than correlation the properties of regression coefficient first of all regression coefficient this is the change in the value of one variable for a unit change in the value of the other variable regression coefficient it is called what is the average change in one variable for a unit change in the other way for example if we change one unit in advertisement how many unit change in sales this is called regression coefficient so we have two regression coefficient
10:53 b x y and b y x b x y is called the regression coefficient of x 1 y what is x 1 y i'll explain now and b y x is the regression coefficient of y on x now see regression analysis consists of two variables one variable is dependent variable other variable is independent variable we can treat suppose we are having two variables x and y so we can treat x as dependent and y as independent or x as independent y as dependent anyone we can treat it as dependent variable and other independent variable so we have two regression lines
11:39 one is called regression line of x on y regression line of y of x what is regression line it's a graphic relationship graphic presentation of the relationship graphic presentation of the relationship between two variables when you put the data on a graph paper we get a straight line denoting the average relationship between the two variables the two regression lines are there regression line of x and y and regression line of y on x regression line x on y is used to predict x for a given value of y so x on y will be used to predict x for any given value of i and y on x will be used to predict y
12:26 for a given value of x for a given value of x so two regression lines are there regression equations the regression equations are so that will be called regression equation the purpose of both are same this is lines are graphical lines whereas regression equations are algebraic equations by using mathematical functional relationship we can make regression equations just like we have two regression lines we will have two regression equations
13:11 one regression equation is x on y and the other regression equation is y on x right now regression coefficient just now i told you regression coefficient means the number of units change in one variable due to a unit change in the other variable so before making this regression equation before making the regression equation you must know you must know how to calculate regression coefficient regression coefficient easily we can find out the regression equations right the regression coefficient of formulas first we will find out regression coefficient of x and y regression coefficient of
13:57 x on y it will be denoted as b x y b small x small y b x y this represents regression coefficient of x one y is equal to r r is the standard symbol for correlation coefficient it's a symbol of correlation coefficient so r into sigma x by sigma y standard deviation of x divided by standard deviation of y so if in the problem correlation is given standard deviation of x series and standard deviation of y series is given then we apply this formula to get b x y right now if r value and start equations are not given in the problem
14:44 only single values are given x values are given y values are given and we have to find out the regression coefficient then the formula will be summation small x y divided by summation y problem values small r standard deviations are given we apply this formula if in the problem our values standard equations are not given but individual values are given figures are given then we apply this formula to find out vxy but this formula will be applied when deviations are taken from actually the first of all
15:31 you have to calculate the mean value if the mean value is in a whole number then we take the deviation from actual mean and we apply this one they can mean a whole number many a time you will calculate the mean and you will get fractions you will get the mean in points then we will take the assumed mean we will take the deviations mean and take the deviations from assume mean so assume means the deviations linger the formula will be this one b x y is equal to summation d x d y
16:17 minus summation of dx into summation d y by n your numerator this is the numerator and denominator summation d y square minus summation d y whole square by n the above formula is used when deviations are taken from assumed so if the deviations are taken from assumed mean this one if the deviations are taken from actual mean this one and when r value and sigma x sigma y is given this one so these are the formulas given for regression coefficient of x on y similarly regression coefficient of violence just now we have calculated x or y no y of x similar formula slide
17:05 b y x b y x means regression coefficient of violence b x y comma the regression coefficient of x y x is equal to r into sigma y by sigma x so compare it and see what is the difference here when we are calculating b x y first value is x so numerator is x when the first value is x numerator is x well if the first letter is y the numerator is y that you have to remember d x y is equal to r into sigma x by sigma y
17:56 first numerator maybe y r into sigma y by sigma x that's it this is the regression coefficient of y on x similarly b y x b y x is equal to summation x y divided by summation x square now you compare it the numerator is same b x y k a or b y x square numerator summation x y here also summation x y but the denominator is different here x y denominator number first one x n see carefully first is x so denominator we should take y when we are having x denominator you should take y here we are having y
18:43 so denominator will take x opposite that way you can remember the numerator will be same summation x y summation x y numerator is same denominator that is the difference right now we'll continue so now see here when we are calculating b x y the first word first alphabet is x so denominator we are going to take why here it is x denominator y here it is y so denominator we are taking x the summation x y numerator will remain same denominator will be opposite x y square this formula will be applied when
19:29 we have taken the deviations from actual mean right similarly when we take the deviations from assumed mean mean calculated numerator will remain same summation d x d y minus summation d x into summation d y by n same thing summation d x d y minus summation d x into summation d y by n denominator will be opposite number b x y when we have taken b x y denominator is y square summation d y square minus summation d y whole square
20:16 square minus submission dx whole square by n when deviations are taken from assumed mean so in this way we calculate regression coefficients after calculating regression coefficient we'll calculate regression equation of x 1 y x 1 y k formula x minus x bar is equal to b x y into y minus y bar this is called regression equation of x on y so when we apply this x and y when we want to predict x given right similarly regression equation of y on x this will be applied to predict to y
21:02 when the value of x is given the formula is y minus y bar is equal to b y x x minus x bar where x bar and y bar are the actual mean chart deviations so these are the regression equations these regression formulas we have to apply so again i repeat before finding out the regression equations of x 1 y and y on x we need to calculate regression coefficients we can be able to apply the formula for regression equations now some properties of regression coefficient
21:48 your regression coefficient of bx y or by xa which properties in the first property both the regression coefficient must show the same sign same sign other b x y positive y x be positive x y negative the b y x b negative both must show positive or both must show negative a positive negative it should never happen one positive or negative both should be positive or both should be negative correlation
22:37 if both regression coefficients are negative then r will also be negative that is one property second property if one of the regression coefficient is more than one the other regression coefficient must be less than one other one for example if bxy is 2.5 then by x should be zero point other b two point b x by two point five r or it is possible that both the regression
23:22 coefficient may be less than one or if one is more than one the other should be less than one but both regression coefficient can never be more than one more than one third next property is if you multiply the regression coefficients and put it under root you will get correlation coefficient other b x y or b y x into b y x don't multiply if you multiply both the regression coefficient and put it under root you will get the value of r r means correlation coefficient the correlation coefficient of formula
24:42 so this is the theory regarding the regression analysis the hope you understood the concept regression means regression analysis is a statistical technique which is concerned with finding out the functional relationship or average relationship between two variables it will be used for prediction purpose the two variables will be one dependent one independent so we can find out the dependent variable for any given value of the independent variable so independent advertisement is independent and sales are dependent we can predict sales for any given value of advertisement similarly in case of agriculture and production and rainfall
25:28 is independent agricultural production is dependent so we can find out agricultural production for a given amount of rainfall these are called regression analysis so we have completed the theoretical part inshallah in the next video we'll start the problems on regression analysis so if you like my lecture please share it in your groups and if you have not subscribed till now please subscribe my channel i want that more and more students can be benefited from my channel so next uh video i'll start the problems on regression analysis
