Question

To investigate the relationship between amount of sales y (in thousands of dollars) and the amount x (in hundreds of dollars) spent on advertising, a marketing researcher chooses eight cities of approximately equal populations and spends differing amounts on advertising in each city. The sales y and the amount x spent on advertising are recorded for each city. From the data the least squares prediction line is: = 24.45 + 2.38x.
Interpret the slope of the least squares line.
(A) For each additional hundred dollars spent on advertising, sales are predicted to increase by $2,380.
(B) If no money is spent on advertising, sales are predicted to be $24.45.
(C) For each additional hundred dollars spent on advertising, sales are predicted to increase by $24,452.
(D) For each additional $1000 dollars in sales, the amount spent on advertising is predicted to increase by $238.

Answer 1

Answer:

(A) For each additional hundred dollars spent on advertising, sales are predicted to increase by $2,380.

Step-by-step explanation:

Regression isa statistical equation, denoting relationship between independent (causal) variable(s) & dependent (effected) variable.

y = a + bx

where y = dependent variable, x = dependent variable, a (intercept) = autonomous value of y, b (slope) = change in y due to change in x

Regression equation of independent variable (x) as advertising expenditure & dependent variable (y) sales : y = 24.45 + 2.38x

Sales are in thousands of dollars, advertising expenditure is in hundreds of dollars. So, the interpretations are :

• Intercept interpretation : When there is zero advertising expenditure, sales are 24.45 thousands i.e $24450
• Slope Interpretation : When advertisement expenditure change (rise) by 1 hundred, sales change (rise) by 2.38 thousand i.e $2380