Data Regression

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Answer Key & Explanations

Data Regression · Grade 11 · Worksheet 1

1. Kaia is analyzing the relationship between study time and test scores for her math class. She collected data from 11 students and found the linear regression equation to be y = 1.7x + 63, where x is study time in hours and y is the test score. If a student studied for 5 hours, what would be the predicted test score? Answer: C. 71.5 Solution: The regression equation is y = 1.7x + 63 Substitute x = 5 into the equation: y = 1.7(5) + 63 Calculate 1.7 × 5 = 8.5 Add 8.5 + 63 = 71.5 The predicted test score is 71.5 The correct answer is 71.5.
   Full step-by-step solution

   Step 1: The regression equation is y = 1.7x + 63 Step 2: Substitute x = 5 into the equation: y = 1.7(5) + 63 Step 3: Calculate 1.7 × 5 = 8.5 Step 4: Add 8.5 + 63 = 71.5 Step 5: The predicted test score is 71.5 The correct answer is 71.5.

2. Sophia is analyzing the relationship between study time and test scores. She collected data from 8 students and found the linear regression equation to be y = 7.2x + 58.3, where x represents study time in hours and y represents the test score. If a student studies for 9 hours, what test score does the regression model predict? Answer: 123.1 Solution: The regression equation is y = 7.2x + 58.3 Substitute x = 9 (study time in hours) into the equation y = 7.2(9) + 58.3 Calculate 7.2 × 9 = 64.8 Add 64.8 + 58.3 = 123.1 The predicted test score is 123.1
   Full step-by-step solution

   Step 1: The regression equation is y = 7.2x + 58.3 Step 2: Substitute x = 9 (study time in hours) into the equation Step 3: y = 7.2(9) + 58.3 Step 4: Calculate 7.2 × 9 = 64.8 Step 5: Add 64.8 + 58.3 = 123.1 Step 6: The predicted test score is 123.1

3. Emma is analyzing the relationship between study time and test scores. She collects data from 5 students: Student A studied 15 minutes and scored 55, Student B studied 30 minutes and scored 70, Student C studied 45 minutes and scored 85, Student D studied 60 minutes and scored 100, and Student E studied 75 minutes and scored 115. Using linear regression, what test score would Emma predict for a student who studies 90 minutes? Answer: 130 Solution: Examine the data points: (15,55), (30,70), (45,85), (60,100), (75,115) Calculate the slope: From (15,55) to (30,70), the score increases by 15 when study time increases by 15 minutes.
   Full step-by-step solution

   Step 1: Examine the data points: (15,55), (30,70), (45,85), (60,100), (75,115) Step 2: Calculate the slope: From (15,55) to (30,70), the score increases by 15 when study time increases by 15 minutes. Slope = 15/15 = 1 Step 3: Find the y-intercept: Using point (15,55), y = mx + b → 55 = 1(15) + b → 55 = 15 + b → b = 40 Step 4: Write the regression equation: y = 1x + 40 Step 5: Predict for 90 minutes: y = 1(90) + 40 = 90 + 40 = 130 The answer is 130.

4. Emma is analyzing the relationship between study time and test scores. She collected data from 10 students and found the linear regression equation to be y = 2.5x + 65, where x is study time in hours and y is the test score. If a student studies for 8 hours, what test score does the regression model predict? Answer: 85 Solution: The regression equation is y = 2.5x + 65 Substitute x = 8 (study time in hours) into the equation y = 2.5(8) + 65 Calculate 2.5 × 8 = 20 Add 20 + 65 = 85 The predicted test score is 85
   Full step-by-step solution

   Step 1: The regression equation is y = 2.5x + 65 Step 2: Substitute x = 8 (study time in hours) into the equation Step 3: y = 2.5(8) + 65 Step 4: Calculate 2.5 × 8 = 20 Step 5: Add 20 + 65 = 85 Step 6: The predicted test score is 85

5. Mere is analyzing the relationship between study time and test scores in her math class. She collected data from 6 students and calculated the linear regression equation as y = 2.4x + 68, where x represents study time in hours and y represents the test score. If a student studies for 5 hours, what test score does the regression model predict? Answer: 80 Solution: The regression equation is y = 2.4x + 68 Substitute x = 5 (hours of study time) into the equation y = 2.4(5) + 68 Calculate 2.4 × 5 = 12 Add 12 + 68 = 80 The predicted test score is 80
   Full step-by-step solution

   Step 1: The regression equation is y = 2.4x + 68 Step 2: Substitute x = 5 (hours of study time) into the equation Step 3: y = 2.4(5) + 68 Step 4: Calculate 2.4 × 5 = 12 Step 5: Add 12 + 68 = 80 Step 6: The predicted test score is 80

6. Matiu collected data on the number of hours students studied for their physics test and their test scores. He found the linear regression equation to be y = 6x + 58, where x is the study time in hours and y is the test score. If a student studied for 4 hours, what score would the regression equation predict? Answer: 82 Solution: The regression equation is y = 6x + 58, where x is study time and y is test score. We're told the student studied for 4 hours, so x = 4.
   Full step-by-step solution

   Step 1: The regression equation is y = 6x + 58, where x is study time and y is test score. Step 2: We're told the student studied for 4 hours, so x = 4. Step 3: Substitute x = 4 into the equation: y = 6(4) + 58 Step 4: Calculate 6 × 4 = 24 Step 5: Add 24 + 58 = 82 Step 6: The predicted test score is 82.