3. The scatterplot given below measures the carats size of diamonds to the price of engagement rings for 30 recent ring sales. Show work **Scatterplot Analysis of Diamond Carat Size and Price**In this educational example, we analyze a scatterplot illustrating the relationship between the carat size of diamonds and the price of engagement rings. The data represents 30 recent ring sales, where:- **x-axis**: Size in Carats- **y-axis**: Price (in dollars)The scatterplot shows a positive correlation, indicating that as the carat size increases, the price also tends to increase.### Graph Explanation- **X-axis (horizontal)**: Represents the size in carats, ranging approximately from 0.10 to 0.35.- **Y-axis (vertical)**: Represents the price of the ring, ranging from $200 to $1000.- **Data Points**: Each point indicates a specific sale, showing the relationship between carat size and price.### Questions and Tasks**a. Correlation Coefficient (r):**Which of the following could be the value of r?- Options: -0.309, 0.675, 0.996, -0.996, -0.675**b. Regression Line Equation:**Given the regression line has a slope of 1230.5 and a y-intercept of 100.5, formulate the slope-intercept equation of the regression line.**c. Prediction Using Regression Line:**Use the regression line to predict the y-value for the x-value 0.20 carats.This analysis helps in understanding the linear relationship and making predictions about diamond pricing based on carat size.

Name: 3. The scatterplot given below measures the carats size of diamonds to
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 3. The scatterplot given below measures the carats size of diamonds to the price of engagement rings for 30 recent ring sales. Show work **Scatterplot Analysis of Diamond Carat Size and Price**In this educational example, we analyze a scatterplot ill

(a) Identify the correlation value for the given scatter plot. The correlation value for the given scatter plot is determined below as follows: From the given scatter plot, it is clear that the most of the points are close together around the straight line and also the regression line is moving towards upper right from left of the x– axis it indicates that there is positive relationship between the variables. Therefore, the scatter plot that matches the correlation value is 0.675. Correct option: 0.675.(b) Determine the slope intercept equation of the regression line. The slope intercept equation of the regression line is obtained below as follows: From the information, given that the value of slope is 1230.5 and the value of y-intercept is 100.5 The required slope intercept equation of the regression line is, (c ) Predict the y-value for the X-value 0.20. The Predicted the y-value for the X-value 0.20 is obtained below as follows: The Predicted the y-value for the X-value 0.20 is 346.6.