c. how many years had attendance within one - standard deviation above or below the mean?\nd. look at the…

Explanation:

Step1: Analyze the problem context

The problem involves analyzing data from a scatter - plot, finding the coefficient of correlation, linear regression equation and making predictions. These are tasks related to data analysis.

Step2: Recall relevant concepts

The coefficient of correlation ($r$) measures the strength and direction of a linear relationship between two variables. The linear regression equation is of the form $y = a+bx$ where $a$ is the y - intercept and $b$ is the slope. However, since no data (scatter - plot values, etc.) is provided in the question, we cannot perform actual calculations. But the general steps for finding the coefficient of correlation involve calculating the covariance of the two variables and their standard deviations, and for the linear regression equation, we use formulas based on the means, variances and covariances of the data points.

Step3: Prediction step

To predict the number of students using the linear regression equation, we substitute the appropriate value (in this case related to the year) into the equation $y = a + bx$.

Answer:

Since no data is provided, we cannot give numerical answers. But the general approach for part c: Count the number of years where the data points on the scatter - plot appear to follow a linear pattern. For part d: Calculate the coefficient of correlation using the formula $r=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\sum_{i = 1}^{n}(y_{i}-\bar{y})^{2}}}$. For part e: Use the least - squares method to find the linear regression equation $y=a + bx$ where $b=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}$ and $a=\bar{y}-b\bar{x}$. For part f: Substitute the appropriate value of $x$ (related to the year) into the linear regression equation $y=a + bx$ to predict the number of students.