The regression equation Y = 60 -0.15X shows sales (V) at a proposed advertising budget (X). (a) Interpret the meaning of the intercept (b) Interpret the meaning of the slope coefficient (c) Predict the sales if the company proposes an advertising budget of Rs. 10 crore. (a) Which of the following is the correct interpretation of the intercept? value by 60. O A The Y-intercept 60 implies that 1 unit increase in X is estimated to increase increase the O B . The Y-intercept 60 implies that when the value of X is the mean value of Y is 60 O C . The Y-intercept 0.15 implies that when the value of X is the mean value of Y is 0.15 OD. The Y-intercept 60 implies that the average value of Y is 60. (b) Which of the following is the correct interpretation of the slope coefficient? O A. The slope coefficient – 0.15 implies that the average value of Y is 0.15. O B. The slope coefficient -0.15 implies that for each unit increase in the value of Y is estimated to decrease by 0.15 units. nr Tha enne mirant-n 15 ime that for unit ins in the Vie schmalarininh 15mie Click to select your answers OF TU (completo) The regression equation Y = 60 -0.15X shows sales (Y) at a proposed advertising budget (X). (a) Interpret the meaning of the intercept. (b) Interpret the meaning of the slope coefficient (c) Predict the sales if the company proposes an advertising budget of Rs. 10 crore. U U T O PUUDE WORT VON AU , WIDT VOIVO U VU. OC. The Y-intercept 0.15 implies that when the value of X is 0the mean value of Y is 0.15. OD. The Y-intercept 60 implies that the average value of Y is 60. (b) Which of the following is the correct interpretation of the slope coefficient? O O O O A. The slope coefficient -0.15 implies that the average value of Y is 0.15. B. The slope coefficient – 0.15 implies that for each unit increase in X, the value of Y is estimated to decrease by 0.15 units. C. The slope coefficient -0.15 implies that for each unit increase in X, the value of Y is estimated to increase by 0.15 units. D. The slope coefficient -0.15 implies that for each unit increase in X, Y also increases by the same unit. (c) If the company proposes an advertising budget of Rs 10 crores, the expected sales is crore. Click to select your answer(s).
The Correct Answer and Explanation is:
Let’s go through each part of the question step-by-step for the regression equation:
Regression Equation:
Y = 60 – 0.15X, where
- Y = Sales (in crores)
- X = Advertising budget (in crores)
(a) Interpretation of the Intercept
The intercept is the constant term in the regression equation, which is 60. It represents the predicted value of Y (sales) when X (advertising budget) is 0.
✅ Correct Answer:
B. The Y-intercept 60 implies that when the value of X is 0, the mean value of Y is 60.
📝 Explanation:
The intercept of 60 means that if the company spends Rs. 0 crore on advertising, the expected sales would be Rs. 60 crore. This gives a baseline level of sales even in the absence of advertising. In regression analysis, the intercept helps us understand the starting value of the dependent variable before the influence of the independent variable is factored in.
(b) Interpretation of the Slope Coefficient
The slope is the coefficient of X, which is -0.15. It represents the change in Y for a one-unit increase in X.
✅ Correct Answer:
B. The slope coefficient -0.15 implies that for each unit increase in X, the value of Y is estimated to decrease by 0.15 units.
📝 Explanation:
The slope -0.15 tells us that for every additional Rs. 1 crore spent on advertising, the sales are expected to decrease by Rs. 0.15 crore. This negative relationship is counterintuitive, as we usually expect higher advertising to lead to higher sales. However, it could indicate over-saturation, ineffective advertising strategy, or diminishing returns on investment.
(c) Predicting Sales for Rs. 10 Crore Advertising Budget
Using the equation: Y=60−0.15×10=60−1.5=58.5Y = 60 – 0.15 \times 10 = 60 – 1.5 = 58.5
✅ Answer:
The expected sales = Rs. 58.5 crore
📝 Explanation:
If the company spends Rs. 10 crore on advertising, the predicted sales would be Rs. 58.5 crore. This again reflects the negative relationship shown in the regression equation: increasing advertising appears to reduce sales, which might suggest a need to revisit the marketing strategy.
Summary:
- Intercept = 60 ➝ Sales with no advertising is Rs. 60 crore.
- Slope = -0.15 ➝ Each extra Rs. 1 crore in advertising reduces sales by Rs. 0.15 crore.
- Predicted sales at Rs. 10 crore advertising = Rs. 58.5 crore
This analysis raises concerns about the effectiveness of advertising, suggesting further investigation is needed.
