Analyzing Residuals and Scatter Plots in Linear Contexts

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. If a customer drives 100 miles, what is the total cost? Analyze the residuals if the predicted cost is $35. Is the prediction accurate?

• $35

• $25

• $30

• $40

In a science experiment, the temperature of a substance was recorded every hour. The data points are (1, 20), (2, 25), (3, 30), (4, 35). Create a scatter plot and determine the line of best fit. What does the slope represent?

• The slope shows the average temperature over the entire duration.

• The slope indicates the maximum temperature reached during the experiment.

• The slope represents the rate of change of temperature with respect to time, which is 5 degrees per hour.

• The slope represents the total temperature after four hours.

A gardener measures the height of plants over a month. The heights (in cm) are recorded as follows: Day 1: 10, Day 2: 15, Day 3: 20, Day 4: 25. Create a scatter plot and find the line of best fit. What is the equation of the line?

• y = 3x + 8

• y = 4x + 6

• y = 2x + 10

• y = 5x + 5

A student scores 70, 75, 80, and 85 on four tests. If the student wants to find a linear relationship between test number and score, create a scatter plot and determine the line of best fit. What are the residuals for each test?

• [5, 5, 5, 5]

• [10, 10, 10, 10]

• [15, 15, 15, 15]

• [0, 0, 0, 0]

A local gym records the number of members each month: January: 50, February: 60, March: 70. Create a scatter plot and determine the line of best fit. Analyze the residuals for March if the predicted number of members is 75. Is the prediction accurate?

• The prediction is exactly correct.

• The prediction is accurate.

• The prediction is not accurate.

• The prediction is slightly off.

A school is collecting data on the number of hours students study and their test scores. If the data points are (1, 60), (2, 70), (3, 80), (4, 90), create a scatter plot and find the line of best fit. What does the y-intercept represent?

• The y-intercept indicates the maximum test score a student can achieve.

• The y-intercept represents the minimum test score possible.

• The y-intercept represents the expected test score when a student studies for 0 hours.

• The y-intercept shows the average study hours of all students.

A restaurant tracks the number of customers each day. On Monday, they had 30 customers, Tuesday 40, and Wednesday 50. Create a scatter plot and determine the line of best fit. What is the predicted number of customers for Thursday?

• 80

• 70

• 50

• 60

A farmer records the amount of fertilizer used and the crop yield. If the data points are (1, 10), (2, 20), (3, 30), create a scatter plot and find the line of best fit. Analyze the residuals for a predicted yield of 25 when 2.5 units of fertilizer are used.

• The residual is 5.

• The residual is 10.

• The residual is 0.

• The residual is -5.