Question

Briefly write the answers by your own words to the following questions:
i) What name is given to the variable that is being estimated in a regression equation?
ii) What is the purpose of an independent variable in regression analysis?
iii) What is the name of the graph that is used to display the relationship between the dependent
(30p.)
variable and the independent variable?
iv) What is the name given to the method used to find the regression coefficients?
v) Explain the strength and direction of the association between two variables, x and y, that have a
correlation coefficient of −0.78.
vi) What are the most important assumptions of the linear regression analysis?

Answer 1

Answer:

Given Data

i) What name is given to the variable that is being estimated in a regression equation.

The variable that is being estimated in a regression equation is called response variable or dependent variable or response variable . The dependent variable is a variable under study which is influenced by two or more independent variables.

ii) What is the purpose of an independent variable in regression analysis.

The purpose of an independent variable is to explain the variation in the dependent/ response variable.

These variables are treated as explanatory variables in regression analysis . These variables helps to study variation or causes in an experiment.we study the influence of independent variables on dependent or response variable . A single dependent variable is not sufficient to study regression since it is based on several independent variables .

therefore we need independent variables while studying regression analysis.

iii) What is the name of the graph that is used to display the relationship between the dependent
variable and the independent variable.

Scatter plot is used to display the relationship between the dependent and the independent variable.This graph is used to display the relationship between dependent variable and the independent variable.  Scatter plots are useful to study the strength and direction of linear relationships from pattern of plotted dots we can identify strength & direction of linear relationship between dependent & independent variables.

iv) What is the name given to the method used to find the regression coefficients.

The regression coefficients are found by the method of least sqaures. To find regression coefficients we use a least square method or Residual sum of squares method. we determine the value of regression coefficient .

v) Explain the strength and direction of the association between two variables, x and y, that have a correlation coefficient of −0.78.

Correlation coefficient varies between -1 to 1. A value close to 0 indicates weak relationship whereas a value close to 1 indicates a strong relationship. Positive value indicates positive correlation wheras negative value indicates negative correlation.

Thus -0.78 indicates that there is a strong negative correlation between the two variables.

vi) What are the most important assumptions of the linear regression analysis.

The most important assumption for linear regression is that there is a strong linear relationship bwtween the dependent variable and the independent variable.The independent variables are uncorrelated. Residual are also uncorrelated.

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