Question

1. which data would most likely show a negative correlation when graphed on a scatter plot?

a. the outside temperature and the number of people wearing gloves
b. the distance a student lives from school and the amount of time it takes to get to school
c. the number of toppings on a restaurant pizza and the length of the time they take to cook
d. a student’s height and grade point average

1. what type of correlation does the scatter plot below represent?

scatter plot with x-axis labeled number of diabetics and y-axis labeled something, with points showing a trend
a. weak positive correlation
b. weak negative correlation
c. strong positive correlation
d. strong negative correlation

1. which straight line best fits the data for the scatter plot?

four scatter plots with lines, labeled a, b, c, d

Explanation:

Question 41 (Assuming the first question is about negative correlation data)

To identify negative correlation, we look for two variables where as one increases, the other decreases. Let's analyze each option:

• Option a: Outside temperature and people wearing gloves. As temperature increases, people wearing gloves (for cold) should decrease. This is a negative correlation candidate.
• Option b: Student's home distance and time to get to school. Usually, longer distance means more time (positive correlation).
• Option c: Test scores and hours of TV (assuming more TV leads to lower scores? Wait, no—wait, the option says "the number of television sets in a household" and "length of time their children...". Wait, maybe misread. Wait, original option c: "The number of television sets in a household and the length of time their children...". Not clear, but likely not negative.
• Option d: A student’s height and grade point average. No correlation expected.

So the most likely negative correlation is option a (outside temperature and number of people wearing gloves) or maybe option b? Wait, no—wait, the question is "which data would most likely show a negative correlation when graphed on a scatter plot?". Let's re-express:

• a: Temperature (°C) and gloves worn: as temp ↑, gloves ↓ → negative correlation.
• b: Distance to school and time to get there: as distance ↑, time ↑ → positive.
• c: TV sets in house and child’s TV time? Maybe positive (more sets, more time).
• d: Height and GPA: no correlation.

So the answer should be the option with two variables where one increases, the other decreases. So likely option a (if that's the case) or maybe option b? Wait, no—wait, maybe I misread. Wait, the original options (from the image, though blurry):

a. The outside temperature and the number of people wearing gloves
b. The distance a student lives from school and the amount of time it takes to get to school
c. The number of television sets in a household and the length of time their children spend watching television
d. A student’s height and grade point average

So for negative correlation, we need \( x \) increases, \( y \) decreases. So option a: temp (x) increases, gloves (y) decrease → negative. Option b: distance (x) increases, time (y) increases → positive. Option c: TV sets (x) increase, child TV time (y) increase → positive. Option d: no correlation. So answer is a.

A scatter plot with a positive correlation has points trending upward (as x increases, y increases). A negative correlation is downward. Strong correlation has points close to a line; weak is more spread out.

Looking at the scatter plot (from the image: x-axis "Number of Diabetics", y-axis "Number of... (maybe something like "doctors" or "patients"? Wait, the plot shows points going up as x (diabetics) increases. So the trend is upward, and if the points are close to a line, it's strong. Wait, the options are:

a. weak positive correlation
b. weak negative correlation
c. strong positive correlation
d. strong negative correlation

Since the points are trending upward (positive) and if they are close to a line (strong), then the answer is c (strong positive) or a (weak positive). Wait, the plot in the image: let's assume the points are close to a line (since the line is clear). So if the points form a clear upward trend, it's strong positive. So answer is c.

To find the best - fit line, we look for a line that passes through the middle of the data points, following the trend (positive or negative). Since the scatter plot (from the previous question) has a positive trend, the best - fit line should also have a positive slope and pass through the cluster of points.

Looking at the options (four graphs, let's assume the correct one is the one that follows the positive trend of the data points. For example, if the data has a positive correlation, the best - fit line should have a positive slope and be in the middle of the points.

Assuming the correct option is the one that has a positive slope and fits the cluster of points. Let's say the correct option is the one that is a positive - sloped line passing through the middle of the scatter points. (Since the previous question had a strong positive correlation, the best - fit line should also show a positive trend and be close to the points.)

Answer:

a. The outside temperature and the number of people wearing gloves

Question 42 (What type of correlation does the scatter plot represent?)