Interpret the slope and intercept of the linear regression model:2. An increase of 1 point in Score on Vault is associated with a(n) ?ofin Score on Balance Beam.3. A gymnast who received a score of 0 points in Score on Vault would have an expected score ofin Score on Balance Beam.4. Which of the following is the correlation coefficient for the linear relationship between Score on Balance Beam and Score on Vault?O A. -0.4169Ов.-0.1738OC. 0.1738O D. 0.41695. What are the null and alternative hypotheses to test if there is a linear relationship between Score on Balance Beam and Score on Vault?O A. Ho : b1ОВ. Но : В 3 bi vs. Ha : Bi # biос. Но : ВO D. Ho : B1= 0 vs. HA : b1 # 0= 0 vs. HA : B1 # 0= 0 vs. HA : B, > 06. Based on the computer output, what is the test statistic for the test in part 5?Test statistic:7. Based on the computer output, the results of the hypothesis test tell us that we have?evidence that therev a linear relationship between Score on Balance Beamand Score on Vault.8. In 2018, Naomi Visser recieved a score of 13.466 on the vault apparatus. Calculate the estimated value for this gymnast's score on balance beam that is predicted by the linear model.Estimated value =9. Naomi Visser's actual score on balance beam that year was 13.8. Use this information and your result from part 8 to calculate the residual for this gymnast.Residual =10. Use information from the computer output to calculate a 99% confidence interval for the slope, B1, of the regression line predicting Score on Balance Beam from Score on Vault.IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places. Stick the landing - Elite female gymnasts compete on 4 apparatus: Floor, Vault, Uneven Bars, and Balance Beam.Simone is investigating the relationship between gymnasts' scores on the different apparatus. She collects a random sample of 75 gymnasts who competed in international competitions between theyears 2006 and 2019. For this problem we will look at the scores for the two apparatus, vault and balance beam.Simone constructs a linear regression model using Score on Vault as the explanatory variable and Score on Balance Beam as the response variable. A scatterplot of Simone's data is shown.Elite Womens Gymnastics13.514.014.515.015.5Score on VaultSimone uses statistical software to fit a linear model to the data. A summary of that model fit is given below:CoefficientsEstimateStd Errort valuePr( > [t])(Intercept)3.5112.6631.3190.191Score on Vault0.72830.18593.9180.000199Residual standard error: 0.908 on 73 degrees of freedomMultiple R-squared: 0.1738, Adjusted R-squared: 0.16241. Use the computer output to write the estimated linear regression equation for predicting Score on Balance Beam from Score on Vault.ŷ =+Score on Balance Beam11121314 1591

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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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The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, 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 Bone Density34 35745 34148 33160 32965 325 Step 3 of 6: Determine the value of the dependent variable yˆ at x=0.
Let price denote a price index for the goods sold by a restaurant, advert the amount spent on advertising, sales the sales for the restaurant, and consider the following two regressions First regression: sales = B1 + B2price + B3price? + B4advert + ßsadvert? + e, Second regression: sales = B1 + B2price + B3price? + e We estimate both regressions using a sample of 105 observations. The sum of square residuals (E ê) from the first regression equals 50, while the sum of square Li=1 residuals from the second regression equals 70. Suppose we are interested in testing the null hypothesis that expected sales do not depend on advertising. What is the F- statistic for this null hypothesis? Recall the F-statistic is given by ((SSER - SSEU)/J)/(SSEy/(n – K)). O a. -15 O b. 42 Oc. 21 O d. 20 O e. All other options are incorrect.
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Is It Getting Harder to Win a Hot Dog Eating Contest?Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available in HotDogs. The figure below shows the scatterplot with the regression line. Year Hot Dogs 2015 62 2014 61 2013 69 2012 68 2011 62 2010 54 2009 68 2008 59 2007 66 2006 54 2005 49 2004 54 2003 45 2002 50 Winning number of hot dogs in the hot dog eating contest Winning number of hot dogs and buns Click here for the dataset associated with this question. (a) Is the trend in the data mostly positive or negative? Positive Negative (b) Using the figure provided, is the residual larger in 2007 or 2008?Choose the answer from the menu in accordance to item (b) of the question statement 20072008 Is the residual positive or…
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, 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 Bone Density34 35745 34148 33160 32965 325 Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1259 vehicles in the government's 2019 Fuel Economy Guide give the regression line highway mpg = 8.720 + (0.914x city mpg) for predicting highway mileage from city mileage. 1 O Macmillan Learning (b) What is the intercept? Give your answer to three decimal places. intercept: Why is the value of the intercept not statistically meaningful? The value of the intercept is an average value calculated from a sample. The value of the intercept represents the predicted highway mileage for city gas mileage of 0 mpg, and such a prediction would be invalid since 0 is outside the range of the data. The value of the intercept represents the predicted highway mileage for slope 0. O The value of the intercept represents the predicted city mileage for highway gas mileage of 0 mpg, and such a car does not exist. mpg
A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. Data were collected that show the number of new customers added during each quarter between 2015 and 2018. A multiple regression model was developed with the number of new customers as the dependent and the following four independent variables: Period (1, …, 16): A variable that measures the trend; Q1 = 1 for first quarter, Q1 = 0 otherwise; Q2 = 1 for second quarter, Q2 = 0 otherwise; Q3 = 1 for third quarter, Q3 = 0 otherwise. Questions: 1. Explain each of the four slopes (Period, Q1, Q2, Q3). 2. How many new customers would you expect in the second quarter of the following year (2019)?
well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days. He started the collection of data of weekly sale of water and the average weekly temperature. Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with you. sales 75 77 69 63 79 80 77 70 73 87 72 73 80 80 69 84 77 72 74 81 temperature 32 36 31 31 34 29 32 35 28 31 30 31 29 35 36 28 32 33 32 33 Sale is in thousand liters and temperature is in degree Celsius. Data is Normally distributed You are required to determine the following information for some concrete decision: Determine the…
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, bo + 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. a Answer How to enter your answer (opens in new window) Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places. 9 S e $ A A Hours Unsupervised Overall Grades V 96 5 t 8 b Oll 0 0.5 1 3.5 4 5 5.5 95 92 85 83 81 73 63 h → U İ 8 i k N 9 O alt I * Р ctri Tables Copy Data Keypad Keyboard Shortcuts Previous step answers…
A well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days. He started the collection of data of weekly sale of water and the average weekly temperature. Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with you. sales 75 77 69 63 79 80 77 70 73 87 72 73 80 80 69 84 77 72 74 81 temperature 32 36 31 31 34 29 32 35 28 31 30 31 29 35 36 28 32 33 32 33 Sale is in thousand liters and temperature is in degree Celsius. Data is Normally distributed You are required to determine the following information for some concrete decision: Determine the…
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 20 31 22 29 39 22 30 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 20 31 22 29 39 22 30 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…

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