**Understanding Regression Analysis: A Practical Example**The table below provides data on the number of hours spent unsupervised each day and the corresponding overall grade averages for seven middle school students. Using this data, you can explore the concept of a regression line, represented by the equation:\[\hat{y} = b_0 + b_1x\]This equation is used to predict the overall grade average based on the number of unsupervised hours each day. **Data:**| Hours Unsupervised | Overall Grades ||--------------------|----------------|| 0 | 87 || 1 | 86 || 1.5 | 79 || 3 | 78 || 4 | 76 || 4.5 | 67 || 5.5 | 65 |**Note:**Keep in mind, the correlation coefficient may not be statistically significant. It’s important not to rely on the regression line for predictions if the correlation is not significant.**Task:***Step 6 of 6:* Calculate the coefficient of determination (\(R^2\)), and round your answer to three decimal places.**Answer:**Provide your answer in the input box provided.This example illustrates how regression analysis can help understand potential relationships between variables, such as time spent unsupervised and academic performance. However, remember to assess the significance of the correlation before making predictions. The table below provides the number of hours spent unsupervised each day and the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, \(\hat{y} = b_0 + b_1x\), 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 | 1.5 | 3 | 4 | 4.5 | 5.5 ||--------------------|----|----|-----|----|----|-----|-----|| Overall Grades | 87 | 86 | 79 | 78 | 76 | 67 | 65 |**Step 5 of 6:** 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 \(\hat{y}\) is given by?- \( b_0 \)- \( b_1 \)- \( x \)- \( y \)

The independent variable is Hours Unsupervised. The dependent variable is Overall Grades. This is…

Answered: The table below gives the number of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables. Here is the data on percent body fat and preferred amount of salt. Preferred amountof salt x 0.2 0.3 0.4 0.5 0.6 0.8 1.1 Percent body fat y 21 30 23 30 39 24 31 In calculating the preferred amount of salt, the weight of the salt was in milligrams. (a) Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in milligrams. (Round your answers to one decimal place.) ŷ = + x (b) A mad scientist decides to measure weight in tenths of milligrams. The same data in these units are as follows. Preferred amountof salt x 2 3 4 5 6 8 11 Percent body fat y 21 30 23 30 39 24 31 Find the equation of the regression line for predicting percent body fat from preferred amount of salt when weight is in tenths of milligrams. (Round your intercept to one decimal place and your slope to two…
Given the equation of a regression line is y= -1.5x-1.8, what is the best predicted value for y given x= -3.0? Assume that the variables x and y have significant correlation.
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The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, y = bo + bjx, for predicting a woman's bone density based on her age. 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. Age 47 49 50 51 58 Bone Density 360 353 336 333 310 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.
The table below gives the number of weeks of gestation and the birth weight (in pounds) for a sample of five randomly selected babies. Using this data, consider the equation of the regression line, y based on the number of weeks of gestation. 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. bo + bjx, for predicting the birth weight of a baby Weeks of Gestation 33 35 37 39 40 Weight (in pounds) 5 6.8 7.9 8.5 9.3 Table Copy Data Step 5 of 6: Find the error prediction when x = 39. Round your answer to three decimal places.
The correlation between X and Y is -.27, and the regression equation is Ŷ = - 0.49X + 9.27 before the data are standardised. A: What is the correlation after the data are standardised? B: What would be the standardised regression equation? A: .27, B: ?̂y = .27?x A: -.49, B: ?̂y = - .49?x + 9.27 A: -.27, B: ?̂y = - .27?x A: -.49, B: ?̂y = - .49?x
The table below gives the number of absences and the overall grade in the class for seven randomly selected students. Based on this data, consider the equation of the regression line, yˆ=b0+b1x , for using the number of absences to predict a student's overall grade in the class. 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. Number of Absences Grade1 3.72 3.33 3.14 2.96 2.47 2.28 1.9 Find the value of the coefficient of determination. Round your answer to three decimal places.
The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, y = bo + b₁x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. 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 Studying 2 3 Midterm Grades 71 72 Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places. Answer How to enter your answer (opens in new window) 4 5 6 73 77 86 Tables Table Copy Data Keypad Keyboard Shortcuts
If a correlation isr= 0.00, then SP = 0 and the regression equation is O Ý =X +0 O Ý =X + X O Ý =0 + X O Ý =Ÿ + 0
The following table presents the orders of Samson Company for the last 36 months (3 years).MonthOrder Year 1Order Year 2Order Year 3January502614712February408592698March491584686April456532644May481599694June511604702July522624724August500612716September510625732October512627740November520650745December536680756Use the data in the above table and regression analysis to forecast the orders for the next 12 months (4th year). Include your excel work sheet and your work in your write up. Show the regression equation, values of intercept, slope, correlation coefficient and coefficient determination and the forecast of orders for the next 12 months.Explain how you could make your forecast’s results more reliable by incorporating a qualitative research to your quantitative results. Previous
The table below gives the number of weeks of gestation and the birth weight (in pounds) for a sample of five randomly selected babies. Using this data, consider the equation of the regression line, ŷ = bọ + b1x, for predicting the birth weight of a baby based on the number of weeks of gestation. 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. Weeks of Gestation 33 34 36 38 41 Weight (in pounds) 6. 6.1 6.8 7.3 7.9 Table Copy Data Step 5 of 6: Find the error prediction when x = 36. Round your answer to three decimal places.

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