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A scatter diagram is given with one of the points drawn in blue​ (large point). The line drawn in red​ (dashed line) is the​ least-squares regression line with the point in blue​ (the large​ point) excluded. The line drawn in blue​ (solid line) is the​ least-squares regression line with the point in blue​ (large point) included. On the basis of these​ graphs, do you think the point in blue is​ influential?
Is the point in blue​ (large point)​ influential? (select one)
(1)No​, because the point significantly affects significantly affects the​ least-squares regression line. 
(2)Yes​, because the point significantly affects significantly affects the​ least-squares regression line. 
(3)Yes,because the point does not significantly affect does not significantly affect the​ least-squares regression line. 
(4)No​, because the point does not significantly affect does not significantly affect the​ least-squares regression line. 

In the graph provided, the large blue point represents a data point that is treated separately for comparison. The red dashed line shows the least-squares regression line excluding the blue point, while the solid blue line represents the least-squares regression line with the blue point included.

To determine whether the point in blue is **influential**, we need to assess how much the blue point affects the slope and intercept of the regression line. Based on your image:

- **If the blue point had a significant impact**, the two regression lines (red dashed and blue solid) would differ greatly. 
- **If the lines are similar**, then the point does not have a major influence.

From the image, it appears that the two lines have a noticeable shift, especially in their slopes. Therefore, the blue point **does significantly affect** the regression line, indicating that it is **influential**.

Thus, the correct answer is:

**(2) Yes, because the point significantly affects the least-squares regression line.**

Would you like further details or explanations on this? 

Here are five related questions you might find helpful:
1. What is an influential point in regression analysis?
2. How do outliers affect the least-squares regression line?
3. What statistical methods can detect influential points?
4. How is the residual value connected to identifying influential points?
5. What are some ways to handle influential points in data?

**Tip:** Always plot your data and compare regression models with and without potential outliers to determine their influence!

A scatter diagram is given with one of the points drawn in blue (large point). The line drawn in red (dashed line) is the least-squares regression line with the point in blue (the large point) excluded. The line drawn in blue (solid line) is the least-squares regression line with the point in blue (large point) included. On the basis of these graphs, do you think the point in blue is influential?

Analyze a scatter plot and determine the influence of a single point on the least-squares regression line. See how the inclusion or exclusion of a data point affects the regression model.

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