Understanding Correlation Strength and Residuals in Data

A teacher collected data on the number of hours students studied and their scores on a test. The line of best fit shows a positive correlation. If a student studied for 5 hours and scored 80, what is the strength of the correlation if the predicted score for 5 hours is 75?

• Weak correlation

• No correlation

• Moderate correlation

• Strong correlation

In a survey, the height of plants was measured over several weeks. The line of best fit indicates a strong positive correlation. If a plant that is 10 cm tall is predicted to grow to 15 cm but actually grows to 12 cm, what is the residual?

• -1 cm

• 5 cm

• 2 cm

• -3 cm

A car rental company analyzed the relationship between the number of days a car is rented and the total revenue. If the line of best fit suggests a strong correlation and a rental for 3 days is predicted to yield $150 but actually yields $130, what does this tell you about the residual?

• The residual is -$20.

• The residual is $0.

• The residual is -$10.

• The residual is $20.

A researcher plotted the relationship between daily exercise in minutes and weight loss in pounds. If the line of best fit shows a moderate correlation and a person who exercised for 30 minutes lost 2 pounds while the predicted loss was 3 pounds, what is the residual?

• 2

• 1

• -1

• 3

In a study of ice cream sales and temperature, the line of best fit shows a strong positive correlation. If the temperature is 85°F and the predicted sales are 200 cones but actual sales are 180 cones, what is the residual?

• -20

• 10

• 200

• -30

A school analyzed the relationship between the number of books read and students' reading comprehension scores. If the line of best fit indicates a weak correlation and a student read 10 books but scored lower than predicted, what does this suggest about the correlation strength?

• The correlation is strong despite the student's low score.

• Reading more books always leads to better comprehension scores.

• The weak correlation implies that reading more books does not guarantee higher comprehension scores.

• The student's score indicates that reading fewer books is more effective.

A local gym recorded the number of members and their average monthly spending. If the line of best fit shows a strong correlation and a member who spends $50 is predicted to spend $60, what is the implication of the residual?

• The residual is -$20, indicating significant under-spending compared to the prediction.

• The residual is -$10, indicating under-spending compared to the prediction.

• The residual is $10, indicating over-spending compared to the prediction.

• The residual is $0, indicating perfect spending according to the prediction.

During a science experiment, the relationship between temperature and the rate of a chemical reaction was plotted. If the line of best fit shows a strong correlation and a temperature of 25°C resulted in a predicted reaction rate of 5 units but the actual rate was 4 units, what is the residual?

• 3 units

• 5 units

• 2 units

• 1 unit

A farmer tracked the relationship between the amount of fertilizer used and crop yield. If the line of best fit indicates a strong positive correlation and the predicted yield for 100 kg of fertilizer is 200 kg but the actual yield is 180 kg, what does this tell you about the residual?

• The residual is -20 kg.

• The residual is 20 kg.

• The residual is 0 kg.

• The residual is -10 kg.

In a study of smartphone usage and sleep hours, the line of best fit shows a negative correlation. If a person uses their phone for 4 hours and is predicted to sleep for 6 hours but actually sleeps for 5 hours, what does this indicate about the correlation strength?

• The correlation strength is strong.

• The correlation strength is likely weak.

• The correlation strength is non-existent.

• The correlation strength is moderate.