Variable Y regresses with variable X with the conditions that \(\overline X = 5.50\), \(\overline Y = 3.50\) and b = 1.50 in the linear regression model (Y = a + bX), where \(\overline Y\) and \(\overline X\) are means of the respective variables and b refers to gradient of line of Y w. r. t X. Which one of the following values of parameter 'a' of the model is correct?

Important Points Linear regression analysis:

• Linear regression analysis is used to predict the value of a variable based on the value of another variable.
• The variable you want to predict is called the dependent variable.
• The variable you are using to predict the other variable's value is called the independent variable.
• This form of analysis estimates the coefficients of the linear equation, involving one or more independent variables that best predict the value of the dependent variable.
• Linear regression fits a straight line or surface that minimizes the discrepancies between predicted and actual output values.
• There are simple linear regression calculators that use a “least squares” method to discover the best-fit line for a set of paired data.
• You then estimate the value of X (dependent variable) from Y (independent variable).

Shortcut Trick

 \(\overline X = 5.50\), 

\(\overline Y = 3.50\) 

b = 1.50 

(Y = a + bX)

Putting the values in the equation, 

3.50 = a + (1.50*5.50)

or, 3.50 = a + 8.25

or, a = -4.75

Hence, the value of 'a' of the model is -4.75