Several states have argued that the 65-mph speed limit has no justification and have refused to enforce it. The federal Department of Transportation (DOT) believes that the 65-mph limit saves lives. To illustrate its contention, the department regressed the number of traffic fatalities (Y) last year in a state on the state’s population (X1), the number of days of snow cover (X2), and the average speed of all cars (X3). The results are shown below. Table 10: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .821 a .780 .613 3.258 a. Predictors: (Constant), population, days of snow, average speed Table 11: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1.4 2.957 .473 .584 Population .00029 .00003 .0034 9.667 .000 Days of Snow 2.4 .62 .759 3.871 .000 Average Speed 10.3 1.1 1.438 9.364 .000 a. Dependent Variable: Number of Traffic Fatalities From the results shown above, write the regression equation. What proportion of variation in the number of traffic fatalities can be explained by the regression model? With all else being equal, how many lives would be saved in a state if the average speed were reduced from 75 to 65 mph? Does reducing the average speed of cars have a statistically significant impact? Explain.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Several states have argued that the 65-mph speed limit has no justification and have refused to enforce it. The federal Department of Transportation (DOT) believes that the 65-mph limit saves lives. To illustrate its contention, the department regressed the number of traffic fatalities (Y) last year in a state on the state’s population (X1), the number of days of snow cover (X2), and the average speed of all cars (X3). The results are shown below.
Table 10: Model Summary
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.821 a |
.780 |
.613 |
3.258 |
|
a. Predictors: (Constant), population, days of snow, average speed |
Table 11: Coefficients
|
Coefficientsa |
||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
|
B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
1.4 |
2.957 |
|
.473 |
.584 |
|
Population |
.00029 |
.00003 |
.0034 |
9.667 |
.000 |
|
|
Days of Snow |
2.4 |
.62 |
.759 |
3.871 |
.000 |
|
|
Average Speed |
10.3 |
1.1 |
1.438 |
9.364 |
.000 |
|
|
a. Dependent Variable: Number of Traffic Fatalities |
From the results shown above, write the regression equation.
What proportion of variation in the number of traffic fatalities can be explained by the regression model?
With all else being equal, how many lives would be saved in a state if the average speed were reduced from 75 to 65 mph?
Does reducing the average speed of cars have a statistically significant impact? Explain.
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