Question

the accompanying data represent the number of days absent, x, and the final exam score, y, for a sample of college students in a general education course at a large state university. complete parts (a) through (e). click the icon to view the absence count and final exam score data. (a) find the least - squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. y = x+ (round to three decimal places as needed.)

Explanation:

Step1: Recall least - squares regression formula

The least - squares regression line is of the form $\hat{y}=b_0 + b_1x$, where $b_1=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^{2}-(\sum_{i = 1}^{n}x_i)^{2}}$ and $b_0=\bar{y}-b_1\bar{x}$, with $\bar{x}=\frac{1}{n}\sum_{i = 1}^{n}x_i$ and $\bar{y}=\frac{1}{n}\sum_{i = 1}^{n}y_i$. First, we need to calculate $\sum_{i = 1}^{n}x_i$, $\sum_{i = 1}^{n}y_i$, $\sum_{i = 1}^{n}x_i^{2}$, $\sum_{i = 1}^{n}x_iy_i$ from the given data set (not shown here).

Step2: Calculate $\bar{x}$ and $\bar{y}$

Let $n$ be the number of data - points. Calculate $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$ and $\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}$.

Step3: Calculate $b_1$

Substitute the sums calculated in Step1 into the formula for $b_1=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^{2}-(\sum_{i = 1}^{n}x_i)^{2}}$.

Step4: Calculate $b_0$

Substitute the values of $b_1$, $\bar{x}$ and $\bar{y}$ into the formula $b_0=\bar{y}-b_1\bar{x}$.

Step5: Write the regression line

The least - squares regression line is $\hat{y}=b_0 + b_1x$.

Since the data is not given in the problem statement, we cannot perform the actual calculations. But the general steps to find the least - squares regression line are as above.

Answer:

Since data is missing, unable to provide numerical values for the regression line coefficients. The regression line is of the form $\hat{y}=b_0 + b_1x$ where $b_0$ and $b_1$ are calculated as described in the steps above.