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In the regression model ( y = a + bx) where x̅ = 2.50, y̅ = 5.50 and a = 1.50 (x̅ and y̅ denote mean of variables x and y and a is a constant), which one of the following values of parameter 'b' of the model is correct?

In the regression model ( y = a + bx) where x̅ = 2.50, y̅ = 5.50 and a = 1.50 (x̅ and y̅ denote mean of variables x and y and a is a constant), which one of the following values of parameter 'b' of the model is correct? Correct Answer 1.60

Key Points

Linear regression model:

  • Linear regression is a way to model the relationship between two variables.
  • You might also recognize the equation as the slope formula.
  • The equation has the form Y= a + bX,
  • where
    • Y is the dependent variable (that’s the variable that goes on the Y-axis),
    • X is the independent variable (i.e. it is plotted on the X-axis),
    • b is the slope of the line and
    • a is the y-intercept.
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Calculation:

( y = a + bx)

where,

  •  x̅ = 2.50
  • y̅ = 5.50
  • a = 1.50
  • (x̅ and y̅ denote mean of variables x and y and a is a constant)

Putting values in the formula:

5.50 = 1.50 + b*2.50

b*2.50 = 4

b = 4/2.5 = 1.60

Therefore, 'B' is the correct answer.

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