Question

#1 In simple linear regression, r is the:

a) coefficient of determination.

b) mean square error.    

c) correlation coefficient.

d) squared residual.

#2 In regression analysis, with the model in the form y = β₀ + β₁x + ε, x is the

a) estimated regression equation.

b) y-intercept.

c) slope.

d) independent variable.

#3 A regression analysis between sales (y in $1,000s) and advertising (x in dollars) resulted in the following equation.

ŷ = 40,000 + 3x

The above equation implies that

a) an increase of $1 in advertising is associated with an increase of $3 in sales.

b) an increase of $2 in advertising is associated with an increase of $3,000 in sales.

c) an increase of $1 in advertising is associated with an increase of $3,000 in sales.

d) an increase of $1 in advertising is associated with an increase of $42,000 in sales.

#4 Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained.

ŷ = 130 − 20x

Based on the above estimated regression equation, if price is increased by 4 units, then demand is expected to

a) increase by 130 units.

b) increase by 80 units.

c) decrease by 20 units.

d) decrease by 80 units.

#5 In a regression analysis, if SSE = 800 and SSR = 400, find the coefficient of determination.

a) 0.333

b) 0.500

c) 0.667

d) 0.800

Answer 1

1. In simple linear regression, r is the correlation coefficient. Thus option c

Note that, the square of r gives the coefficient of determination

2.x is the independent variable. option d

$\beta_{0} : y intercept$

$\beta_{1} : slope$

3. The equation implies that an increase of dollar 1 in advertising, is associated with an increase of dollar 3000 in sales.

Option c

4. If price is increased by 4 units, then demand is expected to decrease by 20 units.

Option c

5. Coefficient of determination can be calculated using the formula

R^2

=Error sum of squares/ Total sum of squares

(Note that error sum of squares is the same as residual sum of squares

And Total sum of squares is the sum of residual sum of squares and regression sum of squares.)

IE. SSE = 800 , SSR = 400 means

Total sum of squares SST = 1200

Thus R^2 = SSE/SST

= 800/1200

=0.667