An air conditioning company located in Central Florida collected data for the number of air conaioning units sold in the Central Florida area and for the outside temperature on the day that sales took place. The Sales Manager put the following table together: Outside Temperature Sales (Number of air conditioning units sold) 3 5 (Degrees F) 68 72 78 81 12 84 15 86 16 89 22 91 93 94 18 19 26 Plot a scatter diagram for the data provided on the table above and the linear regression line calculated in topic (b). Consider that: Y: number of air conditioning units sold X: outside temperature (degrees F) Guidance: graph should look like the one presented in Figure 4.2 of textbook Perform the linear regression calculation and provide the linear regression equation that describes the relationship between Y (number of air conditioning units sold) and X (outside temperature in degrees Fahrenheit. Guidance: follow the steps presented on Table 4.2 of textbook ,Calculate SST, SSE and SSR for this linear regression Guidance: follow the steps presented on Table 4.3 of textbook * Calculate the coefficient of determination (r) and the coefficient of correlation (r). Using the linear regression equation that you developed in topic (b), calculate the estimated sales for a day that will reach 84 degrees F and for a day that will reach 94 F and for both temperature levels calculate the error "e" when comparing the estimated value against the actual data provided. At which of the two temperatures, is your model more accurate? Explain. Calculate an estimate for the variance (o') and the standard deviation for the linear regression model you have developed.
An air conditioning company located in Central Florida collected data for the number of air conaioning units sold in the Central Florida area and for the outside temperature on the day that sales took place. The Sales Manager put the following table together: Outside Temperature Sales (Number of air conditioning units sold) 3 5 (Degrees F) 68 72 78 81 12 84 15 86 16 89 22 91 93 94 18 19 26 Plot a scatter diagram for the data provided on the table above and the linear regression line calculated in topic (b). Consider that: Y: number of air conditioning units sold X: outside temperature (degrees F) Guidance: graph should look like the one presented in Figure 4.2 of textbook Perform the linear regression calculation and provide the linear regression equation that describes the relationship between Y (number of air conditioning units sold) and X (outside temperature in degrees Fahrenheit. Guidance: follow the steps presented on Table 4.2 of textbook ,Calculate SST, SSE and SSR for this linear regression Guidance: follow the steps presented on Table 4.3 of textbook * Calculate the coefficient of determination (r) and the coefficient of correlation (r). Using the linear regression equation that you developed in topic (b), calculate the estimated sales for a day that will reach 84 degrees F and for a day that will reach 94 F and for both temperature levels calculate the error "e" when comparing the estimated value against the actual data provided. At which of the two temperatures, is your model more accurate? Explain. Calculate an estimate for the variance (o') and the standard deviation for the linear regression model you have developed.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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hello I just need help with the last two parts
Transcribed Image Text:**Educational Website Content: Analyzing Air Conditioning Sales Data**
An air conditioning company located in Central Florida collected data for the number of air conditioning units sold in the Central Florida area and for the outside temperature on the day that sales took place. The Sales Manager compiled the following table for analysis:
| Outside Temperature (Degrees F) | Sales (Number of air conditioning units sold) |
|---------------------------------|-----------------------------------------------|
| 68 | 3 |
| 72 | 5 |
| 78 | 7 |
| 81 | 12 |
| 84 | 15 |
| 86 | 16 |
| 91 | 22 |
| 93 | 18 |
| 94 | 19 |
| 94 | 26 |
**Analysis Steps:**
1. **Scatter Diagram and Linear Regression:**
- Plot a scatter diagram for this data and calculate the linear regression line. The goal is to describe the relationship between the dependent variable Y (number of air conditioning units sold) and the independent variable X (outside temperature in degrees Fahrenheit).
- **Guidance:** The graph should resemble Figure 4.2 from the textbook.
2. **Linear Regression Calculation:**
- Perform the linear regression calculation based on the data provided. Deliver the linear regression equation that defines the relationship between Y and X.
- **Guidance:** Follow the procedures detailed in Table 4.2 of the textbook.
3. **Statistical Calculations:**
- Calculate the Sum of Squares for Total (SST), Sum of Squares for Error (SSE), and Sum of Squares for Regression (SSR) for this linear regression.
- **Guidance:** Follow the methods outlined in Table 4.3 of the textbook.
4. **Determining Correlation and Determination:**
- Calculate the coefficient of determination (\(r^2\)) and the coefficient of correlation (r).
5. **Prediction and Error Analysis:**
- Using the linear regression equation from step 2, estimate sales for:
- A day with an expected temperature of 84 degrees F.
- A day with an expected temperature of 94 degrees F.
- Calculate the error "e" by comparing estimated sales against actual sales from the dataset. Determine which temperature forecast provides a more accurate model explanation.
6. **Variance and Standard Deviation
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