Act like a helpful tutor and exlain me :1
2 |ABC Company reports their earnings and expenses data from the years 2004 to 2018 as shown in the table.
3 Use Linear Forecasting and regression to calculate the expense value in the year 2021.
4
5 Years | Earnings | Expenses |
6 2004 $12,340.00 $13,005.00
7 2006 $11,010.00 $9,257.50
8 2008 $14,680.00 $11,010.00
9 2010 $18,350.00 $14,762.50
10 2012 $22,020.00 $16,515.00
11 2014 $25,690.00 $19,267.50
12 2016 $29,360.00 $22,020.00
13 2018 $33,080.00 $29,810.00
14 2021 $25,000.00 222222
15
16 Required:
w
18
19 [Calculate the R-Squared between the known Earnings and Expenses i
20
21 Calculate the slope of the linear regression line between known Earnings and Expenses T
2
23 [Calculate the intercept of the linear regression line between known Earnings and Expenses |
24
25 The full regression equation is:
2% Expenses= | | (Gaming) [| +
27
28 Forecasted Expense in 2021 |
29
Question:
Act like a helpful tutor and exlain me :1
2 |ABC Company reports their earnings and expenses data from the years 2004 to 2018 as shown in the table.
3 Use Linear Forecasting and regression to calculate the expense value in the year 2021.
4
5 Years | Earnings | Expenses |
6 2004 $12,340.00 $13,005.00
7 2006 $11,010.00 $9,257.50
8 2008 $14,680.00 $11,010.00
9 2010 $18,350.00 $14,762.50
10 2012 $22,020.00 $16,515.00
11 2014 $25,690.00 $19,267.50
12 2016 $29,360.00 $22,020.00
13 2018 $33,080.00 $29,810.00
14 2021 $25,000.00 222222
15
16 Required:
w
18
19 [Calculate the R-Squared between the known Earnings and Expenses i
20
21 Calculate the slope of the linear regression line between known Earnings and Expenses T
2
23 [Calculate the intercept of the linear regression line between known Earnings and Expenses |
24
25 The full regression equation is:
2% Expenses= | | (Gaming) [| +
27
28 Forecasted Expense in 2021 |
29
This is AI generated Response.
Asked by: Umesh
Created at: 2025-07-28 22:44:11
Final Answer:
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Did you like this answer?
Absolutely! Let's go step by step to understand each requirement and how you can solve it in Excel or manually.
### 1. **Calculate the correlation between Earnings and Expenses**
The **correlation** measures the strength and direction of a linear relationship between two variables.
**Excel Formula:**
`=CORREL(range_of_Earnings, range_of_Expenses)`
For your data, that would be:
`=CORREL(B6:B13, C6:C13)`
---
### 2. **Calculate the R-Squared between Earnings and Expenses**
**R-Squared** indicates how well data fit a regression line (the proportion of variance explained).
**Excel Formula:**
First, find the correlation, then square it:
`=CORREL(B6:B13, C6:C13)^2`
---
### 3. **Calculate the slope of the linear regression line**
The **slope (m)** shows how much Expenses change per unit change in Earnings.
**Excel Formula:**
`=SLOPE(C6:C13, B6:B13)`
---
### 4. **Calculate the intercept of the linear regression line**
The **intercept (b)** is the value of Expenses when Earnings are zero.
**Excel Formula:**
`=INTERCEPT(C6:C13, B6:B13)`
---
### 5. **The Full Regression Equation**
The regression line equation is:
**Expenses = m \* Earnings + b**
Where:
- \( m \) = Slope (from step 3)
- \( b \) = Intercept (from step 4)
---
### 6. **Forecasted Expense in 2021**
Plug the 2021 Earnings ($25,000) into your regression equation:
`= (Slope) * 25000 + (Intercept)`
---
## **Summary Table**
| Step | Excel Formula | Meaning |
|------|--------------------------------------------------------|---------------------|
| 1 | `=CORREL(B6:B13, C6:C13)` | Correlation (r) |
| 2 | `=CORREL(B6:B13, C6:C13)^2` | R-Squared |
| 3 | `=SLOPE(C6:C13, B6:B13)` | Slope (m) |
| 4 | `=INTERCEPT(C6:C13, B6:B13)` | Intercept (b) |
| 6 | `= (Slope) * 25000 + (Intercept)` | Forecasted Expense |
---
### **If you want to do it manually:**
1. **Calculate the mean of Earnings and Expenses.**
2. **Calculate the covariance of Earnings and Expenses.**
3. **Calculate the variance of Earnings.**
4. **Slope (m) = Covariance(Earnings, Expenses) / Variance(Earnings)**
5. **Intercept (b) = Mean(Expenses) - m * Mean(Earnings)**
6. **Plug in Earnings for 2021 to get predicted Expenses.**
---
**Let me know if you want to see the step-by-step calculation with actual numbers using your data!**
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VIPSolutions
1
2 |ABC Company reports their earnings and expenses data from the years 2004 to 2018 as shown in the table.
3 Use Linear Forecasting and regression to calculate the expense value in the year 2021.
4
5 Years | Earnings | Expenses |
6 2004 $12,340.00 $13,005.00
7 2006 $11,010.00 $9,257.50
8 2008 $14,680.00 $11,010.00
9 2010 $18,350.00 $14,762.50
10 2012 $22,020.00 $16,515.00
11 2014 $25,690.00 $19,267.50
12 2016 $29,360.00 $22,020.00
13 2018 $33,080.00 $29,810.00
14 2021 $25,000.00 222222
15
16 Required:
w
18
19 [Calculate the R-Squared between the known Earnings and Expenses i
20
21 Calculate the slope of the linear regression line between known Earnings and Expenses T
2
23 [Calculate the intercept of the linear regression line between known Earnings and Expenses |
24
25 The full regression equation is:
2% Expenses= | | (Gaming) [| +
27
28 Forecasted Expense in 2021 |
29