Regression Analysis Statistics Complete Chapter in Single Video | Correlation and Regression

Regression analysis statistics all concepts, example and problems for ca, cs, cma, bcom. bba, mcom, UPSC, ssc-cgl, mba, UGC-net and other commerce courses. Video by Chandan Poddar for Grooming education Academy.

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Topics covered:-
00:00 concept of regression analysis
00:43 meaning of regression equation with Example
15:06 Question no – 1 of a Regression equation
31:18 Question no – 2 of a Regression equation
41:47 technical questions of a Regression equation
51:25 mean (Intersection point of two regression equations) from the regression equation
54:40 Impact of change in origin and change in scale of co-efficient of regression equations

REGRESSION ANALYSIS:- In regression analysis, we are concerned with the estimation of one variable for a given value of another variable (or for a given set of values of a number of variables) on the basis of an average mathematical relationship between the two variables (or a number of variables). Regression analysis plays a very important role in the field of every human activity. A businessman may be keen to know what would be his estimated profit for a given level of investment on the basis of the past records.

Simple regression is used to examine the relationship between one dependent and one independent
variable. After performing an analysis, the regression statistics can be used to predict the dependent
variable when the independent variable is known.

◉ The regression line (known as the least-squares line) is a plot of the expected value of the dependent variable for all values of the independent variable. Technically, it is the line that "minimizes the squared residuals". The regression line is the one that best fits the data on a scatterplot.

◉ Using the regression equation, the dependent variable may be predicted from the independent variable. The slope of the regression line (b) is defined as the rise divided by the run. The y-intercept (a) is the point on the y-axis where the regression line would intercept the y-axis. The slope and y-intercept are incorporated into the regression equation. The intercept is usually called the constant, and the slope is referred to as the coefficient. Since the regression model is usually not a perfect predictor, there is also an error term in the equation.

◉ In the regression equation, y is always the dependent variable and x is always the independent variable.

◉ Here is a way to mathematically describe a linear regression model: y = a + bx + e

◉ The significance of the slope of the regression line is determined from the t-statistic. It is the probability that the observed correlation coefficient occurred by chance if the true correlation is zero.

◉ Some researchers prefer to report the F-ratio instead of the t-statistic. The F-ratio is equal to the t-statistic squared.

◉ The t-statistic is equal to the estimated coefficient divided by its standard error.

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