What does the slope and the intercept mean in this setting? **Simple Linear Regression Results**- **Dependent Variable:** Height (inches)- **Independent Variable:** Shoe Size (inches)**Regression Equation:**\[ \text{Height (in)} = 52.293743 + 1.3679745 \times \text{Shoe Size (in)} \]- **Sample size:** 16- **R (correlation coefficient):** 0.72170907- **R-squared:** 0.52086398- **Estimate of error standard deviation:** 2.6920127**Parameter Estimates:**| Parameter | Estimate | Std. Err. | Alternative DF | T-Stat | P-value ||-----------|-----------|------------|----------------|----------|-----------|| Intercept | 52.293743 | 3.4200195 | ≠ 0 | 14 15.290481 | <0.0001 || Slope | 1.3679745 | 0.35065598 | ≠ 0 | 14 3.901187 | 0.0016 |**Analysis of Variance Table for Regression Model:**| Source | DF | SS | MS | F-stat | P-value ||--------|----|-------------|-----------|---------|---------|| Model | 1 | 110.29295 | 110.29295 | 15.21926 | 0.0016 || Error | 14 | 14101.457057 | 7.2469323 | | || Total | 15 | 211.75 | | | |**Graph Explanation:**A scatter plot is provided with shoe size (in inches) on the x-axis and height (in inches) on the y-axis. The blue dots represent the data points, and a red line indicates the fitted linear regression line. The line shows a positive correlation between shoe size and height, suggesting that as shoe size increases, height tends to increase as well.

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Description: What does the slope and the intercept mean in this setting? **Simple Linear Regression Results**- **Dependent Variable:** Height (inches)- **Independent Variable:** Shoe Size (inches)**Regression Equation:**\[ \text{Height (in)} = 52.293743 + 1.36797

Interpret intercept. The intercept is interpreted as follows: Let Y denotes the Height(in),…

Math

Statistics

Simple linear regression results: Dependent Variable: Height (in.) Independent Variable: Shoe Size (in.) Height (in.) = 52.293743 + 1.3679745 Shoe Size (in.) Sample size: 16 R (correlation coefficient) = 0.72170907 R-sq = 0.52086398 Estimate of error standard deviation: 2.6920127 Parameter estimates: Intercept 52.293743 3.4200195 Slope Parameter Estimate Std. Err. AlternativeDF T-Stat P-value +0 1415.290481<0.0001 +0 14 3.901187 0.0016 1.36797450.35065598 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1110.29295110.2929515.21926 0.0016 Error 14101.457057.2469323 Positiu Total 15 211.75 with Fitted line 0.72 Plot Sh in sho Sontee TIses. Close 64in. Shoe. Height (in.) 72 70 68 66 64o 62 60 12 10 Shoe Size (in.) ito

Simple linear regression results: Dependent Variable: Height (in.) Independent Variable: Shoe Size (in.) Height (in.) = 52.293743 + 1.3679745 Shoe Size (in.) Sample size: 16 R (correlation coefficient) = 0.72170907 R-sq = 0.52086398 Estimate of error standard deviation: 2.6920127 Parameter estimates: Intercept 52.293743 3.4200195 Slope Parameter Estimate Std. Err. AlternativeDF T-Stat P-value +0 1415.290481<0.0001 +0 14 3.901187 0.0016 1.36797450.35065598 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1110.29295110.2929515.21926 0.0016 Error 14101.457057.2469323 Positiu Total 15 211.75 with Fitted line 0.72 Plot Sh in sho Sontee TIses. Close 64in. Shoe. Height (in.) 72 70 68 66 64o 62 60 12 10 Shoe Size (in.) ito

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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Question

What does the slope and the intercept mean in this setting?

**Simple Linear Regression Results**

- **Dependent Variable:** Height (inches)
- **Independent Variable:** Shoe Size (inches)

**Regression Equation:**
\[ \text{Height (in)} = 52.293743 + 1.3679745 \times \text{Shoe Size (in)} \]

- **Sample size:** 16
- **R (correlation coefficient):** 0.72170907
- **R-squared:** 0.52086398
- **Estimate of error standard deviation:** 2.6920127

**Parameter Estimates:**

| Parameter | Estimate | Std. Err. | Alternative DF | T-Stat | P-value |
|-----------|-----------|------------|----------------|----------|-----------|
| Intercept | 52.293743 | 3.4200195 | ≠ 0 | 14 15.290481 | <0.0001 |
| Slope | 1.3679745 | 0.35065598 | ≠ 0 | 14 3.901187 | 0.0016 |

**Analysis of Variance Table for Regression Model:**

| Source | DF | SS | MS | F-stat | P-value |
|--------|----|-------------|-----------|---------|---------|
| Model | 1 | 110.29295 | 110.29295 | 15.21926 | 0.0016 |
| Error | 14 | 14101.457057 | 7.2469323 | | |
| Total | 15 | 211.75 | | | |

**Graph Explanation:**
A scatter plot is provided with shoe size (in inches) on the x-axis and height (in inches) on the y-axis. The blue dots represent the data points, and a red line indicates the fitted linear regression line. The line shows a positive correlation between shoe size and height, suggesting that as shoe size increases, height tends to increase as well.

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