MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:### Understanding Regression Analysis in Statistics
#### Objective:
Find the equation of the regression line for the given data. Construct a scatter plot of the data and draw the regression line. Use the regression equation to predict the value of \( y \) for each given \( x \)-value, if meaningful.
#### Data:
The table below shows the caloric content and the sodium content (in milligrams) for 6 beef hot dogs.
| Calories | 150 | 180 | 120 | 130 | 70 | 190 |
|----------|-----|-----|-----|-----|-----|-----|
| Sodium | 410 | 460 | 320 | 380 | 280 | 540 |
#### Tasks:
1. **Find the regression equation:**
- Use the formula: \( \hat{y} = a + bx \) where \( a \) and \( b \) are constants representing the intercept and slope of the line, respectively.
2. **Construct a scatter plot:**
- Plot the given data points on a graph where the x-axis represents the calories and the y-axis represents the sodium content.
3. **Draw the Regression Line:**
- Draw the best-fitting line through the scatter plot which minimizes the distance of all the points from the line.
4. **Predict Values:**
- Use the regression equation to predict sodium content (\( y \)) for the given \( x\)-values:
- (a) \( x = 160 \) calories
- (b) \( x = 80 \) calories
- (c) \( x = 140 \) calories
- (d) \( x = 200 \) calories
**Note:** Round all answers to three decimal places as needed.
#### Implementation:
Enter your answer for the regression equation in the text fields provided and then click "Check Answer" to validate your solution. The screenshot shows an online learning platform where students are instructed to fill in their equations and predictions for interactive learning.
Educational resources like these are vital for understanding statistical concepts and applying them to real-world data.
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This session is based on material from the course IMATH 1530 - 11 (35) and uses "Elementary Statistics: Picturing the World" 7e by Larson as the primary reference.
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