he given table shows a relation between students' attendance percentages and their final grades. Find the best fit linear regression equation, where attendance is the explanatory variable. Round the slope and intercept to two decimal places.

Attendance Percent	Grade
90	94
30	62
40	63
60	70
67	78
70	85
95	96
79	90
54	67
69	74
52	65
83	90
75	89
71	83
85	94
64	74
65	76
71	84
50	64
87	97

Provide your answer below:

y =
x +

To find the best-fit linear regression equation, we need to calculate the slope (\( m \)) and intercept (\( b \)) of the line \( y = mx + b \), where \( y \) is the final grade, and \( x \) is the attendance percentage.

### Step-by-Step Calculation:

1. **Calculate the means** of the attendance percentages (\( x \)) and grades (\( y \)).
2. **Calculate the slope (\( m \))** using the formula:
   
   \[
   m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}
   \]

3. **Calculate the intercept (\( b \))** using the formula:

   \[
   b = \bar{y} - m\bar{x}
   \]

Let's compute these values step-by-step.The best-fit linear regression equation, where attendance is the explanatory variable, is:

\[
y = 0.68x + 33.84
\]

### If you have any questions or need further explanations, let me know!

### Related Questions:
1. How does the slope of the regression line affect the relationship between attendance and grades?
2. What does the intercept of the regression line represent in this context?
3. How can you determine the accuracy of this regression model?
4. What would be the predicted grade for a student with 80% attendance using this model?
5. How can outliers in the data affect the linear regression equation?

**Tip:** The closer the slope is to zero, the weaker the relationship between the two variables.

The given table shows a relation between students' attendance percentages and their final grades. Find the best fit linear regression equation, where attendance is the explanatory variable. Round the slope and intercept to two decimal places.

Discover how to find the best fit linear regression equation for a dataset relating student attendance percentages and final grades. This detailed solution includes calculations for the slope and intercept, using the least squares method. Suitable for high school students studying statistics.

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