**Analyzing Correlation in a Scatterplot****Instructions:**Examine the pattern of all 10 data points in the accompanying scatterplot to determine the strength of correlation between variables x and y.**a. Linear Correlation Assessment:**- Do the data points appear to have a strong linear correlation? - [ ] No - [x] Yes**b. Correlation Coefficient:**- Calculate the correlation coefficient for all 10 data points. - $ r = -0.906 $ - Round your answer to three decimal places as needed.**Additional Information:**- Click the provided link to view a **table of critical values for the correlation coefficient**.**Table of Critical Values:**- A detailed table shows critical values for correlation coefficients based on sample sizes ($ n $).- The table includes values for different significance levels ($ \alpha = 0.05 $ and $ \alpha = 0.01 $).**Example Values:**- $ n = 4 $: $ \alpha = .05 $ -> .950, $ \alpha = .01 $ -> .990- $ n = 10 $: $ \alpha = .05 $ -> .632, $ \alpha = .01 $ -> .765**Options:**- Print or save the table for reference.- Interactive buttons like "Print" and "Done" facilitate navigation.For further assistance, options like "Help me solve this" and "View an example" are available. **Analysis of Linear Correlation**In this exercise, we will explore the concept of linear correlation by examining a scatterplot and calculating the correlation coefficient $ r $.### Steps:1. **Examine the Scatterplot:** - Look at the pattern of all 10 points in the scatterplot. Determine subjectively whether there appears to be a strong linear correlation between the variables $ x $ and $ y $.2. **Calculate the Correlation Coefficient:** - The correlation coefficient, denoted as $ r $, quantifies the degree of linear relationship between two variables. - In this scenario, the calculated value of $ r $ is $-0.906$.3. **Interpretation:** - A correlation coefficient close to -1 or 1 indicates a strong linear relationship. Here, $-0.906$ suggests a strong negative linear correlation.4. **Table of Critical Values:** - A table of critical values is provided for reference to determine the significance level of the correlation coefficient. The table shows the critical values corresponding to various sample sizes and significance levels. - For example, with a sample size of 20, the critical value ranges such as $ .497 $ for a specified level of significance can be referenced to determine if the calculated $ r $ is statistically significant.### Questions:a. **Do the data points appear to have a strong linear correlation?** - Answer: Yesb. **What is the value of the correlation coefficient for all 10 data points?** - $ r = -0.906 $ ### Conclusion:The strong negative correlation is confirmed by both the subjective examination of the scatterplot and the calculated value of the correlation coefficient. This analysis helps in understanding the strength and direction of the relationship between two variables.

Given information: x y 2 9 8 1 8 2 8 3 9 1 9 2 9 3 10 1 10 2 10 3a) Yes the data points appears to have strong correlation. b) Use the given data to form the excel table: X Y X*Y X*X Y*Y 2 9 18 4 81 8 1 8 64 1 8 2 16 64 4 8 3 24 64 9 9 1 9 81 1 9 2 18 81 4 9 3 27 81 9 10 1 10 100 1 10 2 20 100 4 10 3 30 100 9 Sum 83 27 180 739 123 Determine the correlation coefficient using the formula: r=n(∑xy)-∑x·∑yn∑x2-(∑x)2n∑y2-(∑y)2∑X=83,∑Y=27,∑XY=180,∑X2=739,∑Y2=123=10(180)-(83)(27)10(739)-(83)2(10)(123)-(27)2=-0.8802 ≈-0.880 The value of correlation coefficient for all 10 points is - 0.880.c) Use the given data to form the excel table: X Y X*Y X*X Y*Y 8 1 8 64 1 8 2 16 64 4 8 3 24 64 9 9 1 9 81 1 9 2 18 81 4 9 3 27 81 9 10 1 10 100 1 10 2 20 100 4 10 3 30 100 9 Sum 81 18 162 735 42 Determine the correlation coefficient using the formula: r=n(∑xy)-∑x·∑yn∑x2-(∑x)2n∑y2-(∑y)2∑X=81,∑Y=18,∑XY=162,∑X2=735,∑Y2=42=9(162)-(81)(18)9(735)-(81)2(9)(42)-(18)2=0.0 The value of correlation coefficient for all 10 points is 0.0. There is no linear correlation. d) The inclusion of single pair of value influence the correlation of the data set very strongly. After removing this data point the correlation of the data sets drops from - 0.880 to 0.0.