Analyzing Data: Scatter Plots and Regression Models

A researcher collected data on the number of hours students study and their corresponding test scores. Create a scatter plot using the following data: (2, 70), (3, 75), (4, 80), (5, 85). What trend do you observe?

• The trend is fluctuating with no consistency.

• There is a positive trend observed in the data.

• The data shows no clear trend.

• There is a negative trend observed in the data.

Using the data from the previous question, apply a linear regression model to predict the test score for a student who studies for 6 hours. What is the predicted score?

• 80

• 70

• 65

• The predicted score for a student who studies for 6 hours is 75.

A car rental company recorded the distance driven (in miles) and the fuel consumption (in gallons) for various rentals. Create a scatter plot for the following data: (100, 3), (200, 6), (300, 9), (400, 12). What relationship do you see?

• The relationship is linear; fuel consumption increases as distance driven increases.

• Fuel consumption decreases as distance driven increases.

• Fuel consumption remains constant regardless of distance driven.

• There is no relationship between distance driven and fuel consumption.

From the scatter plot created in the previous question, apply a regression model to determine the equation of the line that best fits the data. What is the equation?

• y = ax^2 + c

• y = m + b

• y = mx^2 + b

• y = mx + b (specific values of m and b depend on the data)

A local gym tracks the number of members and the revenue generated each month. The data collected is as follows: (10, 500), (20, 1000), (30, 1500), (40, 2000). Create a scatter plot for this data. What does the plot suggest about the relationship?

• The plot shows a quadratic relationship between the number of members and revenue.

• The plot suggests a positive linear relationship between the number of members and revenue.

• The plot indicates no relationship between the number of members and revenue.

• The plot suggests a negative linear relationship between the number of members and revenue.

Using the gym data, apply a regression model to find the slope and y-intercept. What does the slope represent in this context?

• The slope shows the average weight lifted in the gym.

• The slope indicates the total number of gym visits per week.

• The slope represents the maximum time spent in the gym.

• The slope represents the change in the outcome variable per hour spent in the gym.

A farmer measures the amount of fertilizer used (in pounds) and the yield of crops (in bushels). The data is: (10, 20), (20, 40), (30, 60), (40, 80). Create a scatter plot and describe the trend you see.

• There is no relationship between fertilizer used and crop yield.

• The trend is a positive linear relationship between fertilizer used and crop yield.

• The trend is a negative linear relationship between fertilizer used and crop yield.

• The trend is a quadratic relationship between fertilizer used and crop yield.

Using the farmer's data, apply a regression model to predict the yield if 50 pounds of fertilizer are used. What is the predicted yield?

• Predicted yield based on the regression model for 50 pounds of fertilizer.

• Predicted yield with no fertilizer applied.

• Actual yield from last year's data.

• Predicted yield for 30 pounds of fertilizer.

A school wants to analyze the relationship between the number of extracurricular activities students participate in and their GPA. The data collected is: (1, 3.0), (2, 3.2), (3, 3.5), (4, 3.8). Create a scatter plot for this data. What can you infer from the plot?

• Students with more activities have lower GPAs.

• There is no correlation between extracurricular activities and GPA.

• There is a positive correlation between the number of extracurricular activities and GPA.

• GPA decreases as the number of activities increases.

From the school data, apply a regression model to find the equation that represents the relationship between extracurricular activities and GPA. How can this information be useful for the school?

• The regression model indicates that GPA has no correlation with student engagement.

• The regression equation predicts future GPA without considering extracurricular activities.

• The regression equation shows the relationship between extracurricular activities and GPA, helping the school enhance student performance.

• The school can use the equation to eliminate extracurricular programs entirely.