**Correlation Coefficient Calculation****From the information, given that:**A table with values:| X | Y | X² | Y² | XY ||---|---|---|---|----|| 1 | 3 | 1 | 9 | 3 || 2 | 4 | 4 | 16 | 8 || 3 | 1 | 9 | 1 | 3 || 4 | 5 | 16 | 25 | 20 || 5 | 2 | 25 | 4 | 10 || 6 | 3 | 36 | 9 | 18 || 8 | 6 | 64 | 36 | 48 || 8 | 14| 64 | 196| 112|**Sums:**- ΣX = 36- ΣY = 50- ΣXY = 293- ΣX² = 204- ΣY² = 444**That is:**- \( n = 8 \)- \( \sum x = 36 \)- \( \sum y = 50 \)- \( \sum xy = 293 \)- \( \sum x^2 = 204 \)- \( \sum y^2 = 444 \)**The formula for the correlation coefficient (r) is:**\[r = \frac{\left(\sum xy\right) - \frac{\left(\sum x\right)\left(\sum y\right)}{n}}{\sqrt{\left[\sum x^2 - \frac{\left(\sum x\right)^2}{n}\right] \left[\sum y^2 - \frac{\left(\sum y\right)^2}{n}\right]}}\]Substituting the values:\[r = \frac{(293) - \frac{(36)(50)}{8}}{\sqrt{(204) - \frac{(36)^2}{8}} \cdot \sqrt{(444) - \frac{(50)^2}{8}}}\]Calculations:\[r = \frac{293 - 225}{\sqrt{42} \cdot \sqrt{131.5}}\]\[r = \frac{68}{74. **Part 2: Regression**Based on the correlation you ran to assess the relationship between the number of exposures and perceived connection strength recalled, please carry out the steps to determine the equation for the regression line (or best-fitting line).a. **Step 1**: Find the slope and y-intercept.b. **Step 2**: Using these values, write the equation for the best fitting line, but make sure to write it in terms of the specific predictor (X) and predicted (Y) variables of interest. In other words, your equation should use variable names “# of exposures” and “perceived strength of connection rating”, rather than X and Y.c. Using the regression equation, please predict the perceived connection strength score for a student exposed subliminally to the stranger’s face seven times. Make sure to show your work.d. Using the regression equation, draw the line of best fit on your scatterplot. Please use at least 3 points to anchor your line and show your work. ---**Explanation**:- This section involves calculating a regression line to model the relationship between two variables and using the equation for predictions and visualization.- No graphs or diagrams are included in this text.

Comments: As per the our company guidelines we are supposed to answer only three subparts. Kindly repost other parts in the next question. Solution: Given information: n= 8 Observation ∑x= 36x=∑xn=368=4.5∑y= 50y= ∑yn=508=6.25∑xy= 293∑x2= 204∑y2= 444 a) First we find the slope of the regression equation β1^=n×∑xy- (∑x)×(∑y)n×∑x2-(∑x)2β1^=8×293-36×508×204-362β1^=2344-18001632-1296β1^=544336β1^=1.619048 Now we find intercept of the regression equation β0^=y-β1^×x β0^=6.25-1.619048×4.5β0^=6.25-7.285716β0^=-1.035716 b) The estimated regression line is Strength Score ^= -1.0357+1.6190×Exposures c) To predict the perceived connection strength score for student when exposures is equal to 7 . Strength Score ^= -1.0357+1.6190×Exposures Strength Score ^=-1.0357+1.6190×7Strength Score ^=-1.0357+11.333Strength Score ^=10.2973 The predicted perceived connection strength score for student is 10.2973