You are given the following data.

# of Absences Final
Grade
0 96
1 92
2 71
3 66
4 60
5 51


A. Find the correlation coefficient for the data.
B. Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.

To find the correlation coefficient for the given data, follow these steps:

Step 1: Calculate the mean (average) of both the "Number of Absences" and "Final Grade" columns.
For the "Number of Absences" column:
Mean = (0 + 1 + 2 + 3 + 4 + 5) / 6 = 2.5
For the "Final Grade" column:
Mean = (96 + 92 + 71 + 66 + 60 + 51) / 6 = 72.67

Step 2: Calculate the difference between each data point and the mean for both columns.
For the "Number of Absences" column:
0 - 2.5 = -2.5
1 - 2.5 = -1.5
2 - 2.5 = -0.5
3 - 2.5 = 0.5
4 - 2.5 = 1.5
5 - 2.5 = 2.5

For the "Final Grade" column:
96 - 72.67 = 23.33
92 - 72.67 = 19.33
71 - 72.67 = -1.67
66 - 72.67 = -6.67
60 - 72.67 = -12.67
51 - 72.67 = -21.67

Step 3: Square each difference to eliminate negative values.
For the "Number of Absences" column:
(-2.5)^2 = 6.25
(-1.5)^2 = 2.25
(-0.5)^2 = 0.25
(0.5)^2 = 0.25
(1.5)^2 = 2.25
(2.5)^2 = 6.25

For the "Final Grade" column:
(23.33)^2 = 543.7489
(19.33)^2 = 374.1289
(-1.67)^2 = 2.7889
(-6.67)^2 = 44.4889
(-12.67)^2 = 160.4689
(-21.67)^2 = 470.4089

Step 4: Multiply the corresponding squared difference values for each row.
For each row:
(-2.5) * 23.33 = -58.325
(-1.5) * 19.33 = -29.0
(-0.5) * (-1.67) = 0.835
(0.5) * (-6.67) = -3.335
(1.5) * (-12.67) = -19.005
(2.5) * (-21.67) = -54.175

Step 5: Calculate the sum of the multiplied values from Step 4.
Sum of multiplied values = -58.325 + -29.0 + 0.835 + -3.335 + -19.005 + -54.175 = -164.025

Step 6: Calculate the sum of the squared differences for each column.
For the "Number of Absences" column:
Sum of squared differences = 6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25 = 17.5

For the "Final Grade" column:
Sum of squared differences = 543.7489 + 374.1289 + 2.7889 + 44.4889 + 160.4689 + 470.4089 = 1596.0264

Step 7: Calculate the square root of the product of the sum of squared differences for each column.
Square root of ((Sum of squared differences of "Number of Absences") * (Sum of squared differences of "Final Grade")) = sqrt(17.5 * 1596.0264) = sqrt(27901.4616) = 166.9575

Step 8: Calculate the correlation coefficient (r).
Correlation coefficient (r) = (Sum of multiplied values from Step 5) / (Square root of the product of the sum of squared differences for each column from Step 7)
Correlation coefficient (r) = (-164.025) / (166.9575) = -0.981

Therefore, the correlation coefficient for the given data is approximately -0.981.

To find the equation for the regression line and predict the final grade of a student who misses 3.5 days, follow these steps:

Step 1: Calculate the slope of the regression line (b).
Slope (b) = (r * (Standard Deviation of "Final Grade")) / (Standard Deviation of "Number of Absences")

Step 2: Calculate the y-intercept of the regression line (a).
y-intercept (a) = (Mean of "Final Grade") - (b * (Mean of "Number of Absences"))

Step 3: Substitute the values from Steps 1 and 2 into the equation y = a + bx to obtain the equation for the regression line.

Step 4: Use the equation for the regression line to predict the final grade of a student who misses 3.5 days by substituting the value of 3.5 for x in the equation and calculating the corresponding y-value.