XYZ Corporation is analyzing the effects of several independent variables on its annual sales revenue using multiple regression analysis. The regression model takes the form: $$ Sales = \beta_0 + \beta_1 Price + \beta_2 Advertising + \beta_3 Seasonality + \epsilon $$ Where: $$ Sales $$ = Annual Sales Revenue in thousands of dollars $$ Price $$ = Selling price per unit in dollars $$ Advertising $$ = Expenditure on advertising in thousands of dollars $$ Seasonality $$ = A dummy variable representing seasonal effects (1 if high season, 0 otherwise) $$ \beta_0, \beta_1, \beta_2, \beta_3 $$ are the coefficients to be estimated After fitting the model, the following coefficients were estimated: $$ \beta_0 = 50 $$, $$ \beta_1 = -2 $$, $$ \beta_2 = 3 $$, $$ \beta_3 = 20 $$. What does the coefficient $$ \beta_1 $$ indicate, and what is the implication for pricing strategy based on this coefficient?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Interpreting Regression Coefficient for Pricing Strategy

Very Hard Multiple Regression Analysis Regression Coefficients

XYZ Corporation is analyzing the effects of several independent variables on its annual sales revenue using multiple regression analysis. The regression model takes the form:

$$ Sales = \beta_0 + \beta_1 Price + \beta_2 Advertising + \beta_3 Seasonality + \epsilon $$

Where:

$$ Sales $$ = Annual Sales Revenue in thousands of dollars
$$ Price $$ = Selling price per unit in dollars
$$ Advertising $$ = Expenditure on advertising in thousands of dollars
$$ Seasonality $$ = A dummy variable representing seasonal effects (1 if high season, 0 otherwise)
$$ \beta_0, \beta_1, \beta_2, \beta_3 $$ are the coefficients to be estimated

After fitting the model, the following coefficients were estimated: $$ \beta_0 = 50 $$, $$ \beta_1 = -2 $$, $$ \beta_2 = 3 $$, $$ \beta_3 = 20 $$. What does the coefficient $$ \beta_1 $$ indicate, and what is the implication for pricing strategy based on this coefficient?

The coefficient $$ \beta_1 = -2 $$ indicates that for every dollar increase in price, annual sales revenue increases by $2, suggesting a strategy to raise prices.

The coefficient $$ \beta_1 = -2 $$ indicates that for every dollar increase in price, annual sales revenue decreases by $2, suggesting a price reduction strategy.

The coefficient $$ \beta_1 = -2 $$ is not statistically significant, so it is irrelevant to pricing strategies.

Hint

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