A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 2000 for each of the 52 cities randomly selected in the US. The data included information on the followingvariables: Deaths: The number of deaths in traffic accidents per city and Income: The median income per cityAs part of his study, he ran the following simple linear regression model as pictured : Question: Based on the above results, the researcher tested the hypotheses ( Null: B1=0 versus Alternative: B1 not equal to 0) using T test. What do we know about the test statistic of the test, what is the approximate p-value, and value of Rsquared? And based on your result, what is your conclusion? Show your work for full credit. ### Fitting a Linear Model Using Least Squares**Model Equation:**\[ \text{Deaths} = \beta_0 + \beta_1 (\text{Income}) \]This model was fit to the data using the method of least squares. The following results were obtained from SAS:#### Table: Analysis of Variance| Source | Sum of Squares | df ||--------|----------------|----|| Model | 711680 | 1 || Error | 50692661 | 50 |- **Model**: Represents the variability explained by the regression model.- **Error**: Represents the variability not explained by the model.- **df (degrees of freedom)**: Relates to the number of data points and the number of parameters estimated.#### Table: Parameter Estimates| Variable | Parameter Estimate | Standard Error of Parameter Estimate ||----------|--------------------|--------------------------------------|| Constant | 292.518 | 823.505 || Income | 0.05 | 0.06 |- **Constant**: The intercept of the model, indicating the predicted number of deaths when income is zero.- **Income**: The slope of the model, showing the change in the number of deaths per unit increase in income.- **Standard Error**: Reflects the accuracy of the parameter estimates.

Given: Dependent variable is Deaths. Independent variable is the median income per city. Based on…

Answered: A researcher is investigating possible…

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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A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 2000 for each of the 52 cities randomly selected in the US. The data included information on the following
variables: Deaths: The number of deaths in traffic accidents per city and Income: The median income per city
As part of his study, he ran the following simple linear regression model as pictured :

Question: Based on the above results, the researcher tested the hypotheses ( Null: B1=0 versus Alternative: B1 not equal to 0) using T test. What do we know about the test statistic of the test, what is the approximate p-value, and value of Rsquared? And based on your result, what is your conclusion? Show your work for full credit.

### Fitting a Linear Model Using Least Squares

**Model Equation:**
\[ \text{Deaths} = \beta_0 + \beta_1 (\text{Income}) \]

This model was fit to the data using the method of least squares. The following results were obtained from SAS:

#### Table: Analysis of Variance

| Source | Sum of Squares | df |
|--------|----------------|----|
| Model | 711680 | 1 |
| Error | 50692661 | 50 |

- **Model**: Represents the variability explained by the regression model.
- **Error**: Represents the variability not explained by the model.
- **df (degrees of freedom)**: Relates to the number of data points and the number of parameters estimated.

#### Table: Parameter Estimates

| Variable | Parameter Estimate | Standard Error of Parameter Estimate |
|----------|--------------------|--------------------------------------|
| Constant | 292.518 | 823.505 |
| Income | 0.05 | 0.06 |

- **Constant**: The intercept of the model, indicating the predicted number of deaths when income is zero.
- **Income**: The slope of the model, showing the change in the number of deaths per unit increase in income.
- **Standard Error**: Reflects the accuracy of the parameter estimates.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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