### Analyzing SO₂ Deposition Rate and Steel Weight Loss#### Data Overview:- **Independent Variable (x)**: SO₂ deposition rate (mg/m²/d)- **Dependent Variable (y)**: Steel weight loss (g/m²)| x | 15 | 18 | 31 | 43 | 45 | 112 ||----|----|----|----|----|----|------|| y | 250| 350| 470| 500| 560| 1170 |### (a) Scatter Plot ConstructionThe scatter plot is constructed to visualize the relationship between SO₂ deposition rate (x-axis) and steel weight loss (y-axis). The plot shows a series of data points scattered across the graph, suggesting an overall positive trend. #### Graphs Explanation:- **Upper Left Plot**: Displays data points with a noticeable upward trend, indicating a potential linear relationship.- **Upper Right Plot**: Shows another arrangement of the data, lacking clear linearity.- **Lower Left Plot**: Demonstrates a scattered distribution, making it difficult to discern a clear pattern.- **Lower Right Plot**: Highlights an outlier with the highest x-value significantly affecting the trend.### Assessment of Linear Regression Model- **Question**: Does the scatter plot show a reasonable linear relationship? - **Choice**: Yes, the scatter plot shows a reasonable linear relationship. ✅### (b) Regression Line Calculation- **Calculate the equation** for the estimated regression line using the data points. All numerical values should be rounded to two decimal places.### (c) Percentage of VariationCalculate the percentage of observed variation in steel weight loss attributed to the model relationship with variation in deposition rate. Round to one decimal place.### (d) Influence of OutliersWhen the largest x-value (112) is excluded, it may significantly influence the regression line. Recalculate the regression equation without this observation and round numerical values to two decimal places.### Comparing Equations- **Question**: Does the new equation differ significantly from the original one? - **Choice**: No, there are not significant differences. ✅This exercise highlights the impact of outliers on linear regression analysis and the importance of visual data interpretation through scatter plots.

Given the data as x y 15 250 18 350 31 470 43 500 45 560 112 1170

The accompanying data was read from a graph. The independent variable is SO2 deposition rate (mg/m²/d) and the dependent variable is steel weight loss (g/m²). x 15 18 31 43 45 112 y 250 350 470 500 560 1170 (a) Construct a scatter plot. y 1200 1000 800 600 400 200 O y 1200 1000 800 600 400 200 20 40 60 20 40 60 80 100 120 80 100 120 X X y 1200 1000 800 x 600 400 200 y 1200 1000 800 600 400 200 20 40 20 40 60 60 80 100 120 80 100 120 Does the simple linear regression model appear to be reasonable in this situation? o Yes, the scatter plot shows a reasonable linear relationship. No, the scatter plot does not show a reasonable linear relationship. X X (b) Calculate the equation of the estimated regression line. (Round all numerical values to two decimal places.) y = (c) What percentage of observed variation in steel weight loss can be attributed to the model relationship in combination with variation in deposition rate? (Round your answer to one decimal place.) % (d) Because the largest x value in the sample greatly exceeds the others, this observation may have been very influential in determining the equation of the line. Delete this observation and recalculate the equation. (Round all numerical values to two decimal places.) y* = Does the new equation appear to differ substantially from the original one (you might consider predicted values)? o Yes, there are significant differences. No, there are not significant differences.

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...