If Linear correlation coefficient r = 0.794556Coefficient of determination = 0.631319Equation of regression line is y = 16.5523 +0.725938xthen both variables are moving in the samedirection.АTrueFalse

The strength and direction of linear relationship between two variables is measured by correlation.

Answered: If Linear correlation coefficient r =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Define regression line
The least-squares regression equation is y=761.7x+13,208 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7483. Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree.
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x�^=�0+�1�. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.050.05 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 3939 2525 1515 4242 4242 2424 3232 2020 3030 3737 Snow Accumulation (in.in.) 66 1515 2929 66 1414 2626 2323 1212 1616 77 Copy Data Regression equation: yˆ=�^= Is the equation appropriate? Yes
The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree.
1)Write the regression equation that represents the above equation. Y = 9.804326378 + 0.65795*X1 + 0.200358 X2 Height of an individual = 9.8043 + 0.6579*Mother's Height + 0.2004* Father's Height 2)Is this a good predictor equation? Why or why not (use appropriate statistics/hypothesis test to prove your point)?
Suppose there is a significant correlation between two variables. Describe a case under which it might be inappropriate to use the linear regression equation for prediction.
If a regression line for two variables has a small positive slope, then the: variables are positively associated? variables are negatively associated? association of the variables cannot be determined. variables have no association with each other.
Explain in simple language why knowing only these correlations enables you to say that prediction of manatee deaths from number of boats registered by a regression line will be much more accurate than prediction of a golfer's second‑round score from his first‑round score. Select the correct explanation from the choices. A) The closer r is to 0 (in either direction), the stronger the linear relationship is between two variables. B) Actually, prediction of manatee deaths from number of boats registered by a regression line will be much less accurate than prediction of a golfer's second‑round score from his first‑round score. C) The fraction of the variation in the observed values of x explained by the least‑squares regression of y on x is given by r. The higher this fraction, the more likely that the prediction is accurate. D) The further r is from 0 (in either direction), the stronger the linear relationship is between two variables.
1.)fill in the blanks. Based on the physician's study, the predictor variable, X is_____and the response variable, Y, is________. 2.) As described in the article, the relation between age and peak heart is a______. - positive relation - negative relation - no relation 3.) Provide the regression line, ŷ=a+bx. Show steps/equations used to get answer. 4.) Suppose a 40 year old person is randomely selected. Use your Model to predict their peak heart rate. 5.) Based on your model, as a person ages one year, how much would you expect peak heart rate to change?
Last ride Consider the roller coasters described inExercise 26 again. The regression analysis gives themodel Duration = 64.232 + 0.180 Drop.a) Explain what the slope of the line says about howlong a roller coaster ride may last and the height of thecoaster.b) A new roller coaster advertises an initial drop of200 feet. How long would you predict the rides last?c) Another coaster with a 150-foot initial drop advertisesa 2-minute ride. Is this longer or shorter than you’dexpect? By how much? What’s that called?
Use RStudio to fit a simple linear regression model to the data below. Please submit a copy of your code and any appropriate output (a photo/screenshot will be sufficient). 300? Is the fitted linear regression model What is the 95% prediction interval for xo = appropriate for this data, and which assumption appears to be violated if not? dataset <- data.frame ( с (294, 247, 267, 358, 423, 311, 450, 534, 438, 688, 630, 709, 627, 1021, 615, 700, 999, 1250, 1015, 850, 980, 1650, 1025, 1200, 1500), у 3 с (30, 32, 37, 44, 47, 49, 56, 62, 68, 80, 84, 88, 97, 97, 100, 106, 109, 112, 117, 128, 130, 135, 160, 180, 210) X = %3D
A statistical test that can be performed to determine any significant linear relationship between two quantitative variables is: * A F-test of the null hypothesis that the slope of the regression line is zero. A F-test of the null hypothesis that the correlation is less than -1. A F-test of the null hypothesis that the correlation is greater than 1. A F-test of the null hypothesis that the intercept of the regression line is zero. The coefficient of determination and the slope of the regression line not necessarily have the same signs. TRUE FALSE If the coefficient of determination is calculated as 0.33 and regression equation y = - 2.4 – 3.5x, then the correlation coefficient is_.* 0.1089 0.5745 -0.1089 -0.5745

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If Linear correlation coefficient r = 0.794556 Coefficient of determination = 0.631319 Equation of regression line is y = 16.5523 + 0.725938x then both variables are moving in the same direction. A) True False B