Mastering Linear Regression and Residual Analysis

A researcher collected data on the number of hours students study and their corresponding test scores. The data points are plotted on a scatter plot. If the linear regression equation is found to be y = 5x + 60, where y is the test score and x is the hours studied, what would be the predicted test score for a student who studies for 4 hours?

• 70

• 100

• 80

• 90

In a study of the relationship between the temperature in degrees Celsius and the number of ice creams sold, a scatter plot shows a positive correlation. If the linear regression line is y = 2.5x + 20, how many ice creams are expected to be sold when the temperature is 30 degrees Celsius?

• 95

• 50

• 80

• 110

A car rental company analyzed the relationship between the number of days a car is rented and the total revenue generated. The linear regression equation derived from their data is y = 40x + 100. Calculate the total revenue if a car is rented for 7 days.

• 450

• 300

• 380

• 500

After plotting the data points for the height and weight of a group of students, the linear regression equation is determined to be y = 0.5x + 50. If a student is 160 cm tall, what is the predicted weight according to the regression model?

• 120

• 130

• 150

• 140

A farmer recorded the amount of fertilizer used and the yield of crops. The scatter plot indicates a linear relationship, and the regression equation is y = 3x + 15. If the farmer uses 10 kg of fertilizer, what is the expected crop yield?

• 60

• 30

• 25

• 45

In a survey, the relationship between the number of hours spent on social media and the grades of students was analyzed. The regression line is y = -2x + 90. If a student spends 5 hours on social media, what is the predicted grade?

• 85

• 90

• 80

• 75

A school wants to analyze the relationship between the number of extracurricular activities students participate in and their GPA. The regression equation is y = 0.3x + 2.5. If a student is involved in 4 activities, what is their predicted GPA?

• 3.0

• 2.5

• 4.0

• 3.7

A city planner is studying the correlation between the population of a neighborhood and the number of parks available. The regression equation is y = 0.1x + 5. If a neighborhood has a population of 2000, how many parks are predicted to be available?

• 150

• 250

• 205

• 300

After analyzing the residuals from a linear regression model predicting sales based on advertising spend, the residuals are found to be consistently positive for high advertising spends. What does this indicate about the model's predictions in that range?

• The model's predictions are random for high advertising spends.

• The model accurately predicts sales for high advertising spends.

• The model underestimates sales for high advertising spends.

• The model overestimates sales for high advertising spends.

A scientist is examining the relationship between the amount of rainfall and the growth of a specific plant species. The regression equation is y = 2x + 10. If the residual for a particular data point is -3, what does this tell you about the actual growth compared to the predicted growth?

• The actual growth is 3 units less than the predicted growth.

• The actual growth is equal to the predicted growth.

• The actual growth is 10 units less than the predicted growth.

• The actual growth is 3 units more than the predicted growth.