Answered: 1. Use the computer output to write the…

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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Transcribed Image Text:Fiber and breakfast cereal - In an attempt to learn whether cereals high in fiber are also high in sugar and calories, three researchers took a random sample of 24 brands of breakfast cereal and recorded the calories, sugar (in grams), and fiber (in grams) per serving for each brand. The researchers constructed a linear model using Fiber as the explanatory variable and Calories as the response variable to answer the question, "Can the amount of fiber per serving be used to predict the amount of calories per serving in a given brand of cereal?" A scatterplot is given below. Cereal Fiber and Calories T 4 10 12 Fiber (grams) per serving A linear model is fitted to the data using the statistical software, R, and a summary of that model fit is given below: Coefficients Estimate Std Error value Pr( > |t]) (Intercept) 113.5 3.668 30.939 1.25e-19 Fiber -3.611 0.8085 -4.467 0.000193 001 08 09 Calories per serving

Transcribed Image Text:Residual standard error: 12.817 on 22 degrees of freedom Multiple R-squared: 0.4756, Adjusted R-squared: 0.4517 Round all calculated answers to 4 decimal places. 1. Use the computer output to write the estimated regression equation for predicting amount of calories per serving from the amount of fiber per serving. ŷ = 2. Which of the following is the correlation coefficient for the relationship between fiber and calories? OA. -0.4756 OB. -0.6896 OC. 0.6896 OD. 0.4756 3. Each additional 1 gram of fiber is associated with a(n) ??? V of calories per serving. 4. What is the expected amount of calories per serving for a cereal with 0 grams of fiber? 5. The packaging for the cereal Common Sense Oat Bran has 3 grams of fiber per serving. Calculate the expected value for the number of calories per serving of Common Sense Oat Bran that is predicted by the linear model. expected value = 6. The packaging for Common Sense Oat Bran indicates it has 100 calories per serving. Use this information and your result from part 5 to calculate the residual for this brand of cereal. residual = 7. What are the null and alternative hypotheses to test if there is a linear relationship between Fiber and Calories? ОА. Но : b %3D 0 vs. HA : bi #0 оВ. Но : В 3 O vs. Ha : Bi # 0 ос. Но : В %3 0 vs. HA : Bi > 0 OD. Ho : B1 = bị vs. HA : B1 # bị 8. What is the test statistic and p-value from the test in part 7? Test statistic: and p-value: 9. What do the results of the hypothesis test tell us about the linear relationship between the amount of fiber per serving and the calories per serving in breakfast cereal? OA. There is little evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. OB. There is little evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. OC. There is extremely strong evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. OD. There is extremely strong evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. 10. Calculate a 99% confidence interval for the slope, B1, of the regression line predicting the number of calories per serving from the number of grams of fiber per serving. IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places.

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