In the following exercise, visually check the conditions for fitting a least squares regression line, but you do not need to report these conditions in your solutions.The scatterplot below displays the relationship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years.6020-20Husband's age (in years)4060Given below is summary output of the least squares fit for predicting wife's age from husband's age.EstimateStd. Errort valuePr(>|t|)(Intercept)1.57401.15011.370.1730age_husband0.91120.025935.250.0000df == 168= 1. Use the information(a) We might wonder, is the age difference between husbands and wives consistent across ages? If this were the case, then the slope parameter would be ß,above to evaluate if there is strong evidence that the difference in husband and wife ages differs for different ages. (Round your test statistic to two decimal places.)Using the given point estimate and standard error, we can compute a T score of. Since df168, the p-value is between 0.020 and 0.010 vXTherefore, the data%3Dprovidestrong evidence that the average difference between husbands' and wives' ages differs for different ages.(b) Write the equation of the regression line for predicting wife's age from husband's age. (Enter your answers to four decimal places.)agewx ageH+%D(c) Interpret the slope in context. (Enter your answer to four decimal places.)For each additional year in husband's age, the model predicts an additionalyears in wife's age.Interpret the intercept in context. (Enter your answer to four decimal places.)Men who are 0 years old are expected to have wives who are on averageyears old.Wife's age (in years)

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Description: In the following exercise, visually check the conditions for fitting a least squares regression line, but you do not need to report these conditions in your solutions.The scatterplot below displays the relationship between husbands' and wives' ages

(a)Using the given point estimate and standard error, we can compute a T score of 35.25. Since df =…

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The scatterplot below displays the relationship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. 60- 40- 20 40 60 Husband's age (in years) Given below is summary output of the least squares fit for predicting wife's age from husband's age. Estimate Std. Error t value Pr(>It|) (Intercept) 1.5740 1.1501 1.37 0.1730 age_husband 0.9112 0.0259 35.25 0.0000 df = 168 Wife's age (in years)

The scatterplot below displays the relationship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. 60- 40- 20 40 60 Husband's age (in years) Given below is summary output of the least squares fit for predicting wife's age from husband's age. Estimate Std. Error t value Pr(>It|) (Intercept) 1.5740 1.1501 1.37 0.1730 age_husband 0.9112 0.0259 35.25 0.0000 df = 168 Wife's age (in years)

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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In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Variable DF Estimate SE T Intercept 1 -5.0 0.26 - 19.3 WHIP 1 6.8 0.14 47.4 Which of the following statements is the best interpretation of the value 6.8 shown in the output? ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP. WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA. For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units. For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units. Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.
The data below represents commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute time (in minutes), x 5, 20, 25, 40, 60, 84, 105 Well-being index score, y 69.1, 67.8, 67.1, 66.3, 66.0, 64.3, 62.3 Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. y=___x + ____ (round to three decimal places as needed).
Statistical software is generally used to test the significance of a regression model. The table below shows software output for a least squares regression line. Fill in the blanks with the correct answers, using the table above. Assume a significance level of 0.05. The variable "unemp" is the_______variable. The value of the slope of the regression line is_______. The slope of the regression line is not significantly different from______because the p-value is______ which is larger than 0.05.
Consider the following. X Y 1 3 5 2 9 7 11 7 5 5 (a) Find an equation of the least squares line for the data given above. (Round your numerical values to two decimal places.) y= (b) Draw a scatter diagram for the data and graph the least squares line. y 15 10 5 15 10) Need Help? 2 Pe 10 @O 08 15 10 15 10 10 10 X 5
2. The scatterplot below summarizes husbands' and wives' heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Summary output of the least squares fit for predicting wife's height from husband's height is also provided in the table. Wife's height (in inches) 70 65 60 55 60 65 70 Husband's height (in inches) 75 (Intercept) height husband Estimate Std. Error 43.5755 4.6842 0.2863 0.0686 t value 9.30 4.17 Pr>t) 0.0000 0.0000 Is there strong evidence that taller men marry taller women? State the hypotheses and include any information used to conduct the test... b) Given that R² = 0.09, what is the correlation of heights in this data set? c) You meet a married man from Britain who is 5'9" (69 inches). What would you predict his wife's height to he? How reliable is this prediction? d) You meet another married Brit who is 6'7" (79 inches). Would it be wise to use the same linear model to predict his wife's height? Why or why not?
A researcher records data on 7 adult pairs' heights (in inches) to compare the physical characteristics of brothers and sisters. Brother Sister 71 69 68 64 6 65 67 63 70 65 71 62 66 62 Mean 68.4285 64.2857 SD 2.2253 2.4299 r=0.4050 What would the least-squares regression equation be for predicting the brother's height from the sister's? A. brother's height = 0.037+44.58 * sister's height B. brother's height = 44.58 + 0.371* sister's height C. brother's height = 20.71 + 0.029 * sister's height D. brother's height = 3.28- 40.68 * sister's height If the sister's height is the same as the mean (64.2857 inches), what would the brother's predicted height be A. 68.4285 (the same as the mean as well) B. 62.1234 C. 70.8990 D. None of the above. Which of the following would be correct? A. The pair of means, (68.4285, 64.2857), lies on the linear regression line. B. The effectiveness of the linear regression model is about 16%, C. The effectiveness of the linear regression model is 10096. D. Both…
When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is (picture attached) What is the predicted area of the circle, in cm2, 4 seconds after the stone is dropped? 49.72 cm2 199.43 cm2 311.89 cm2 1854.10 cm2
ghment-Responses/submit?dep3D274217688tags%3Dautosave#question4737280 7 An article gave a scatter plot along with the least squares line of x = rainfall volume (m) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot. 米 6 12 14 20 23 30 40 46 55 67 72 82 96 112 127 y 4 10 13 15 15 25 27 45 38 46 53 75 82 99 104 n USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? O Yes, the scatterplot shows a reasonable linear relationship. O Yes, the scatterplot shows a random scattering with no pattern. O No, the scatterplot shows a reasonable linear relationship. O No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope 0.8535 intercept -2.2338 (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 49. (Round your answer…
The data below represent the number of days absent, x, and the final grade, y, for a sample of college students at a large university. Complete parts (a) through (e) below. No. of absences, x Final grade, y 1 2 3 4 7 8 9 89.0 86.2 83.2 80.8 77.8 73.4 63.8 68.3 65.4 62.6 (a) Find the least-squares regression line treating the number of absences, x, as the explanatory variable and the final grade, y, as the response variable. y = - 3.110 x + ( 89.045 ) (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. For every unit change in the final grade, the number of days absent falls by days, on average. O B. For a final score of zero, the number of days absent is predicted to be days. O C. For every day absent, the final grade falls by on average. O D. For zero days absent, the…