### Regression and Correlation Analysis**Example Problem:**Suppose a doctor measures the height, \( x \), and head circumference, \( y \), of 8 children and obtains the data below. The correlation coefficient is 0.879 and the least squares regression line is \( \hat{y} = 0.216x + 11.540 \). Complete parts (a) and (b) below.**Data:**| Height (\( x \)) | Head Circumference (\( y \)) ||------------------|------------------------------|| 27.75 | 17.6 || 24.5 | 16.9 || 26.75 | 17.1 || 25.75 | 16.9 || 27.5 | 17.5 || 26.25 | 17.2 || 25.75 | 17.4 || 26.75 | 17.4 || 27 | 17.4 |**Questions:**(a) Compute the coefficient of determination, \( R^2 \).\[ R^2 = \_\_\_% \] (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately \(\_\_\_%\) of the variation in \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_) is explained by the least-squares regression model. According to the residual plot, the linear model appears to be \_\_\_\_\_\_\_\_\_\_\_\_\_\_. (Round to one decimal place as needed.)**Explanation:**1. **Coefficient of Determination, \( R^2 \):** The \( R^2 \) value represents the proportion of the variance in the dependent variable (head circumference, \( y \)) that is predictable from the independent variable (height, \( x \)). It ranges from 0 to 1, where: - 0 means the model does not explain any of the variability in the response data around its mean, - 1 means the model explains all the variability in the response data around its mean.2. **Interpretation:** Percentages derived from \( R^2 \): - The closer \( R^2 \

(a) Use EXCEL to determine the value of coefficient of determination. EXCEL procedure: Go to…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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9(20 pts). Correlation analysis and Simple Linear Regression. A study is con- ducted with a group of dieters to see if the number of grams of fat each consumes per day, x, is related to cholesterol level y. The data are shown in Spreadsheet "Question 8": Fat Grams x: 6.8 5.5 8.2 10 8.6 9.1 8.6 10.4 5.9 6.3 7.6 8 8.5 7.9 5.9 6.7 9.1 10.1 9.5 8.9 Cholesterol Level y: 212 192 193 263 222 250 190 249 190 185 192 201 215 189 203 194 241 256 255 245 pole sta ber of of perm lity o n = 20, Στ = 161.6, y = 216.85, Σ Υ = 4337, = 8.08, Σν = 955159. Στ? = 1347.52, Σ y = 35671.5, (a) Compute the value of the correlation coefficient, r, between x and y. (b) Test if the population correlation coefficient p > 0.5 at a = 0.05. (c) Determine the regression line equation y' = a + bx. (d) Predict the cholesterol level of a dieter who consumes x = 8.5 grams of fat per day. (e) Find the 90% prediction interval of the cholesterol level of a person who consumes x=8.5 grams of fat per day. at mo 9 mally tribu…
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + 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 0.5 2 3 4.5 Overall Grades 99 98 96 92 89 88 80 Table Copy Data Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. E Click the icon to view the data table. ked Бcor (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. (Round the slope to three decimal places and round the constan ion estion 4 Number of Number of tion Number of Male Fatal Licensed Drivers Crashes Number of Female Fatal Licensed Drivers (000s) Crashes Age (000s) (Males) (Females) 74 4,803 2,022 5,375 973 Enter your answer in the edit fields and then click Check Ans Print Done parts remaining
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, yˆ=b0+b1x, 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 3 4 5 Overall Grades 95 92 85 81 62 Table Step 3 of 6 : Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, 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 0.5 2 3 4.5 5 6 Overall Grades 99 98 96 92 89 88 80 Table Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.
Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.904 and the least squares regression line is y=0.208x+11.736. Complete parts (a) and (b) below.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + bx, 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 1.5 3 4 4.5 5.5 Overall Grades 87 86 79 78 76 67 65 Table Copy Data Step 4 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. N Prev E Tables E Keypad Answer Keyboard Shortcuts a True O False © 2021 Hawkes Learning JIS A
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. 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. Price in Dollars 106 108 117 181 193 Number of Bids 10 15 16 17 18 Table Find the estimated y-intercept and correlation coefficient ..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 seven randomly selected middle school students. Using this data, consider the equation of the regression line, ŷ = bo + bịx, 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 0.5 1.5 2.5 3 4 4.5 Overall Grades 89 86 81 79 72 67 62 Table Copy Data Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is 0.780 and the least squares regression line is y=0.169x + 12.739. Complete parts a and b below. Height, x Head Circumference, y (a) Compute the coefficient of determination, R². R² =% (Round to one decimal place as needed.) 27.00 17.4 25.75 17.1 26.75 17.1 ... 25.50 17.1 27.75 17.5 26.75 17.1 26.25 17.2 27.00 17.3 5
The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+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 0.5 1 1.5 2 3 3.5 4.5 Midterm Grades 63 66 68 72 74 93 94 Table Step 4 of 6 : Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
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