**Text Transcription and Overview of Graphs**As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities.Your first step in the analysis is to construct a scatterplot of the data.**FIGURE: Scatterplot for U.S. Department of Transportation Problem***Graph Description:*The scatterplot from the U.S. Department of Transportation illustrates the relationship between fatal accident frequency and driver age. The x-axis represents the percentage of drivers under age 21, ranging from 6% to 20%. The y-axis represents the number of fatal accidents per 1000 licenses, ranging from 0 to 4.5. The scatterplot shows a positive trend, suggesting that as the percentage of younger drivers increases, the number of fatal accidents also tends to increase.Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear regression analysis. The results are as follows:**TABLE: Linear Regression Output for U.S. Department of Transportation Problem**| Coefficients | Standard Error | t Statistic | p-value ||------------------|----------------|-------------|---------|| Intercept | -1.5974 | 0.3717 | -4.2979 | 0.0001 || Percent Under 21 | 0.2871 | 0.0294 | 9.7671 | 0.0000 |This table provides the linear regression coefficients and statistics. The intercept is -1.5974, while the coefficient for the percentage of drivers under 21 is 0.2871. The low p-values (0.0001 and 0.0000) indicate statistically significant relationships. **Educational Text on Linear Regression Analysis**Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear regression analysis. The results are as follows:**TABLE. LINEAR REGRESSION OUTPUT FOR U.S. DEPARTMENT OF TRANSPORTATION PROBLEM**| Coefficients | Standard Error | t Statistic | p-value ||--------------------|----------------|-------------|---------|| Intercept | -1.5974 | 0.3717 | -4.2979 | 0.0001 || Percent Under 21 | 0.2871 | 0.0294 | 9.7671 | 0.0000 |The p-value for "Percent under 21" in the regression output is $ p = 0.0000 $. The t-test for significance in simple linear regression is:- $ H_0: \beta_1 = 0 $- $ H_a: \beta_1 \neq 0 $**Use alpha = 0.05. What does the p-value tell you about the estimated regression line?**- $ p = 0.0000 $ indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and $ H_0 $ should be rejected.**Explanation of Graph:**The scatter plot in the image displays the relationship between the "Percentage of drivers under age 21" and the "Fatal accidents per 100,000 drivers." A positive correlation is evident, suggesting that as the percentage of young drivers increases, the number of fatal accidents also increases. This visual observation is supported by the linear regression analysis findings.Linear regression analysis helps to quantify the strength and type of relationship between two variables, providing critical insights for decision-making and policy formulation.

P value is the value that indicates the probability of the null hypothesis being correct. It is used in regression analysis of check whether null hypothesis should be accepted or rejected.Option p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be rejected is correct. Explanation: Given that, the null and alternative hypotheses for the slope test are, Null Hypothesis : H0: β1 = 0Alternative Hypothesis : Ha: β1 ≠ 0 p-value for this test is, p = 0.0000 Since, p-value = 0.0000 is less than 0.05 level of significance, we reject the null hypothesis (H0) and conclude that the the slope of the estimated regression equation is different from zero.