The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for five randomly selected middle school students. Using this data, consider the equation of the regression line, ŷ = b, + b,x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0 1 2 35 Overall Grades 98 84 78 74 63 Summation Table xy xy x2 y? Student 10 98 0 0| 9604 Student 2 1 84 84 1 7056 Student 3 2 78 156 4 6084 Student 4 3 74 222 9 5476 Student 5 5 63 315 25 3969 Sum 11 397 777 39 32189 Step 1. Find the estimated slope. Round your answer to three decimal places. Answer: Step 2. Find the estimated y-intercept. Round your answer to three decimal places. Answer: Step 3. Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. 5 of 6 Step 4. Determine the value of the dependent variable ŷ at x = 0. Step 5. According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable ŷ is given by? Step 6. Find the value of the coefficient of determination. Round your answer to three decimal places.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for five randomly selected middle school students. Using this data, consider the equation of the regression line, ŷ = b, + b,x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0 1 2 35 Overall Grades 98 84 78 74 63 Summation Table xy xy x2 y? Student 10 98 0 0| 9604 Student 2 1 84 84 1 7056 Student 3 2 78 156 4 6084 Student 4 3 74 222 9 5476 Student 5 5 63 315 25 3969 Sum 11 397 777 39 32189 Step 1. Find the estimated slope. Round your answer to three decimal places. Answer: Step 2. Find the estimated y-intercept. Round your answer to three decimal places. Answer: Step 3. Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. 5 of 6 Step 4. Determine the value of the dependent variable ŷ at x = 0. Step 5. According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable ŷ is given by? Step 6. Find the value of the coefficient of determination. Round your answer to three decimal places.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Transcribed Image Text:The table below gives the number of hours spent unsupervised each day as well as the
overall grade averages for five randomly selected middle school students. Using this
data, consider the equation of the regression line, ŷ = b, + b,x, for predicting the
overall grade average for a middle school student based on the number of hours spent
unsupervised each day. Keep in mind, the correlation coefficient may or may not be
statistically significant for the data given. Remember, in practice, it would not be
appropriate to use the regression line to make a prediction if the correlation coefficient is
not statistically significant.
Hours Unsupervised 0 1 2 35
Overall Grades
98 84 78 74 63
Summation Table
xy xy x2 y?
Student 10 98 0 0| 9604
Student 2 1 84 84 1 7056
Student 3 2 78 156 4 6084
Student 4 3 74 222 9 5476
Student 5 5 63 315 25 3969
Sum
11 397 777 39 32189
Step 1. Find the estimated slope. Round your answer to three decimal places.
Answer:
Step 2. Find the estimated y-intercept. Round your answer to three decimal places.
Answer:
Step 3. Determine if the statement "Not all points predicted by the linear model fall on
the same line" is true or false.
5 of 6
Step 4. Determine the value of the dependent variable ŷ at x = 0.
Step 5. According to the estimated linear model, if the value of the independent variable
is increased by one unit, then the change in the dependent variable ŷ is given by?
Step 6. Find the value of the coefficient of determination. Round your answer to three
decimal places.
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