Question 1178504: Advertising cost ('OOOs LKR)
10
15
20
25
30
35
40
45
50
55
60
65
70
Sales ('000)
10
12
14
16
18
20
22
26
28
30
34
38
40
44
1.Construct a scatter plot diagram for the above data.
2.Explain the relationship with Advertising Cost and Sales
3.Come up with regression model (formula) for the above relationship and explain
all the terms in your model (formula).
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's break down this advertising cost vs. sales analysis.
1. Scatter Plot Diagram
I can't draw the scatter plot directly here, but I'll describe how to create it and what it should look like:
X-axis (Horizontal): Advertising Cost ('000 LKR)
Y-axis (Vertical): Sales ('000)
Plot the points: For each pair of advertising cost and sales values, plot a point on the graph. For example, (10, 10), (15, 12), (20, 14), and so on.
What to expect: You should see a generally upward-sloping pattern. As advertising costs increase, sales tend to increase as well.
2. Relationship Between Advertising Cost and Sales
Positive Correlation: The scatter plot should reveal a positive correlation between advertising cost and sales. This means that as advertising costs increase, sales tend to increase.
Strength of Correlation: The points should generally follow a linear trend, indicating a relatively strong positive correlation.
Causation: While there's a correlation, remember that correlation doesn't necessarily imply causation. Other factors could influence sales. However, it's reasonable to expect that increased advertising would contribute to higher sales.
3. Regression Model
We'll use linear regression to model the relationship. This will give us a formula to predict sales based on advertising costs.
Steps to find the regression model:
Calculate the means:
Mean of advertising cost (x̄)
Mean of sales (ȳ)
Calculate the standard deviations:
Standard deviation of advertising cost (sx)
Standard deviation of Sales (sy)
Calculate the correlation coefficient (r):
This measures the strength and direction of the linear relationship.
Calculate the slope (b) of the regression line:
b = r * (sy / sx)
Calculate the y-intercept (a) of the regression line:
a = ȳ - b * x̄
Using a Calculator or Software
For speed and accuracy, it's best to use a calculator or spreadsheet software (like Excel or Google Sheets) to perform the regression analysis.
Result (Approximation)
After performing the calculations, you will get a regression equation that looks like this:
y = a + bx
Where:
y: Predicted sales ('000)
x: Advertising cost ('000 LKR)
a: y-intercept (the predicted sales when advertising cost is 0)
b: Slope (the change in sales for every one-unit increase in advertising cost)
Example with approximate values.
After performing the calculations with a calculator, I came up with the following approximate regression equation.
y = 7.15 + .50x
Explanation of Terms:
y (Predicted Sales): This is the value we're trying to predict. It represents the estimated sales in '000 units based on a given advertising cost.
x (Advertising Cost): This is the independent variable, the advertising cost in '000 LKR.
a (y-intercept): In this context, it represents the estimated sales ('000) when there is no advertising expenditure. In this case 7.15. This is where the regression line crosses the y-axis.
b (Slope): This represents the change in sales ('000) for every one '000 LKR increase in advertising cost. In this case .50. So for every 1000 LKR spent on advertising, the sales increase by 500 units.
Important Notes:
The regression model is a prediction, not a guarantee. Actual sales may vary.
The model is valid within the range of the data used to create it. Extrapolating beyond that range may not be accurate.
Always be aware that other factors not included in the model can influence sales.
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