Question

1. sketch a scatterplot with a correlation coefficient close to 0 and one with r close to -1. please label each.

1. which of the following best explains the concept of least squares?

a. the line of best fit is the one with the smallest number of squares.
b. the line of best fit is the one with the smallest sum of squared correlation.
c. the line of best fit is the one with the smallest number of squared predictions.
d. the line of best fit is the one with the smallest sum of the squared residuals.

for questions 11-17, use the following problem:
a group of school-aged children were randomly selected and monitored for one week. the candy that was
eaten was recorded and weighed. the following data was collected.

amount of candy eaten vs. number of cavities

amount of candy eaten (pounds/week)	number of cavities
2	3
1.75	4
1.63	2
0.5	0
0.34	0
1.2	1
2.4	3
3	5

1. sketch a scatterplot showing the relationship of x = amount of candy and y = # of cavities. be sure to label axes.

Explanation:

Step1: Understand the concept of Least Squares

The least - squares method aims to find the line of best fit. The residual for a data point \((x_i,y_i)\) is \(e_i=y_i-\hat{y}_i\), where \(\hat{y}_i\) is the predicted value from the regression line.

Step2: Analyze each option

• Option a: The number of squares is not relevant. The least - squares method is not about counting squares.
• Option b: There is no such thing as “sum of squared correlation” in the context of the least - squares line of best fit.
• Option c: The number of squared predictions is not the basis for the least - squares line.
• Option d: The line of best fit (regression line) in the least - squares method is the one that minimizes \(\sum_{i = 1}^{n}(y_i-\hat{y}_i)^2\), where \((y_i-\hat{y}_i)\) is the residual.

Answer:

d. The line of best fit is the one with the smallest sum of the squared residuals.