Question

• 19. In a linear regression model if the mean of the independent variable data is 10, the mean of the dependent
  

variable data is 75 and the slope is 5, the intercept is

• a. 25
  
• b. 7
  
• c. -25
  
• d. 13
  

• 20. In a linear regression model if the mean of the independent variable data is 10, the mean of the dependent
  

variable data is 75 and the slope is 5, if xequals 15, the forecast, y, is

• a. 75
  
• b. 100
  
• c. 125
  
• d. 150

Answer 1

Ans 19)

Let x be the independent variable and y be the dependent variable.

= Mean of the independent variables = 10

= Mean of the dependent variables = 75

Slope = 5

We will use the equation

where the intercept is 'c' and the slope is 'm'

75 = 5 * 10 + c

c = 75 - 50

c = 25

Hence the intercept is option a.

Ans 20) If,

= Mean of the independent variables = 10

= Mean of the dependent variables = 75

Slope = 5

Then the intercept comes out to be equal to 25 (from above answer)

The linear regression model is given by, y = 5 x + 25

If x = 15,

y = 5 x + 25

y = 5 * 15 + 25

y = 75 + 25

y = 100

Hence the forecast for y is 100, i.e. option b