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- A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) to the right. Height (in.) Head Circumference (in.) O 27 17.4 Data Table 25.5 17.2 26 17.2 25.75 17 Critical Values for Correlation Coefficient 27.75 17.5 26.5 17.2 26.25 17.2 3 0.997 26.75 17.4 4 0.950 0.878 Click here to see the Table of Critical Values for Correlation Coefficient. 0.811 7 0.754 0.707 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): Xi 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9 A linear model was fitted using the statistical software R, producing the following output: Coefficients: (Intercept) 98.81082 -0.75263 Estimate Std. Error t value Pr(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 Signif. codes: 0 ***' 0.001 **** 0.01 0.05 .' 0.1 1 Residual standard error: 4.304 on 8 degrees of freedom Multiple R-squared: 0.9748, F-statistic: 309.7 on 1 and 8 DF, Adjusted R-squared: p-value: 1.11e-07 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using a = 0.01. Use an appropriate P-value from the output given. (Note: R uses…
- The Answer is 3y = -x + 19As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): X 1= average high school grade in mathematics (HSM) X 2 = average high school grade in science (HSS) X 3 = average high school grade in English (HSE) X 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: SOURCE DF MS F VALUE PROB>F MODEL 28.64 5.73 11.69 0001 ERROR 218 106 82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN 0.700 R-SQUARE 0.211 4.635 ADJ R-SQ 0.193 PARAMETER STANDARD T FOR O VARIABLE ESTIMATE ERROR PARAMETER -0 PROB> ITI INTERCEPT 2.327 0.039 5.817 0.0001 0.0003 XI HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV) 0.146 0.037 3.718 a.036 0.038 0.950 0.3432…Are the signs of the coefficients on the variables "Frequency of Flights" and "Destination is a Big City" corresponding to the utility of the "Air" mode meaningful? Utility for Car Utility for Air param. t stat Param. t stat Constant 4.77 6.995 0 fixed Travel Time (mins) -0.03 -16.926 -0.03 -16.926 Travel Cost / Income ($/$) -726.35 -4.28 -726.35 -4.28 Frequency of Flights (per week) 0 fixed 0.12 13.414 Is Destination a Large City 0 fixed 1.5 5.576 Travel Party Size > =2^2 1.75 5.873 0 Fixed
- A residual plot from a simple linear regression analysis is shown to the right. Use the plot to answer the question below. residuals 0 X Which of the following statements regarding the plot is true? OA. The condition that the residuals are normally distributed is not met since not all of the residuals fall on the reference line in the residual plot. OB. The condition that the residuals have constant variation is met since the lines connecting the largest positive residuals and largest negative residuals are parallel. Oc. The condition that the residuals are normally distributed is not met since there is a diamond shape to the residuals in the residual plot. OD. The condition that the residuals have constant variation is not met since the variation increases and then decreases as x gets larger.Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 46 wines, a model was created using the percentages of aloohol to predict wine quality Y-0.337 +0.5635X,, where X, in the alcohol content (%) and Y, is the rated quality of the wine. For these data, Syx 0.9316, X 10.63, and h 0.027260 when X 10. Complete parta (a) throi a. Construct a 05% confidence interval estimate of the mean wine quality rating for all wines that have 10% alcohol. 4.988 spypx= 10 s 5.608 (Type integers or decimals. Round to three decimal places as needed. Use ascending order) b. Construct a 95% prediction interval of the wine quality rating of an individual wine that has 10% alcohol. (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)Experimenters wants to assess the association between X and Y, the scatter plot of X and Y showed a quadratic pattern. After applying the appropriate regression model, experimenters want to produce a prediciton interval for X = 20. Using StatCrunch with 95% confiendence, the result interval is 223 to 267. Provide the most appropriate interpretation of this interval.
- Consider the function f(x) = 2/T + 6 on the interval [4, 9]. Find the average or mean slope of the function on this interval. 0.4 By the Mean Value Theorem, we know there exists a c in the open interval (4, 9) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?