Exercises: Using only the information above (i.e., you are not expected to load thedata into RStudio to do any investigations), respond to the following questions.1. Give the equation of the least square regression line that uses a country's birth rateto predict the life expectancy of its citizens.2. Use your linear model from part 1. to predict the life expectancy in a country with abirth rate of 36 per 1000 people.3. Guinea-Bissau has a birth rate of 36 per 1000 people and a life expectancy of 57.8years. Use the answer in part 2. to find the residual for this data point.4. Is there evidence that birth rate is an effective predictor of life expectancy? Carryout the calculation of the p-value to make an assessment. (Show your work.)5. Find the 99% confidence interval for the slope of the true linear model and interpretthe interval.6. Using the R output above, determine the value of the correlation coefficient. Whatdoes this value tell you about the linear relationship between life expectancy and birthrate? Consider trying to predict the life expectancy of citizens in a country based on the birthrate (per 1000 people) in that country.Here is a scatterplot of the data from a random sample of 50 countries.> ggplot (SampCountries, aes (BirthRate, LifeExpectancy)) +geom_point (color = "darkred")+labs (title = "Life Expectancy by Birth Rate")+Life Expectancy by Birth Rate80 -70 -10203040BirthRateHere is (some of) the R output for the linear model for this data.> LifeBirth.lm <-lm (LifeExpectancy~BirthRate, data=SampCountries)> summary (LifeBirth. lm)Call:Im (formula =LifeExpectancyBirthRate, data = SampCountries)Residuals:Min10Median30Маx-7.0592 -2.30470.91232.50195.8358Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 85.262951.0330182.54BirthRate-0.632910.04492-14.09Residual standard error: 3.424 on 48 degrees of freedomMultiple R-squared:0.8053,Adjusted R-squared:0.8012F-statistic: 198.5 on 1 and 48 DF,p-value: < 2.2e-16LifeExpectancy

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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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Management proposed the following regression model to predict sales at a fast-food outlet. y = ?0 + ?1x1 + ?2x2 + ?3x3 + ? where x1 = number of competitors within one mile x2 = population within one mile (1,000s) x3 = 1 if drive-up window present 0 otherwise y = sales ($1,000s). The following estimated regression equation was developed after 20 outlets were surveyed. ŷ = 10.5 − 4.2x1 + 6.8x2 + 15.5x3 (a) What is the expected amount of sales (in dollars) attributable to the drive-up window? $ (b) Predict sales (in dollars) for a store with two competitors within one mile, a population of 8,000 within one mile, and no drive-up window. $ (c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and a drive-up window. $
A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well rested. The results are shown in the table (picture) for the 8 participants. a. Using the data (picture), calculate and interpret the regression line for the data.
c. What are the 2 main pieces of information you get from the linear regression model? Should I go back to the data set and recalculate slope and y intercept if I already have determined the equation of the trend line?
Imagine Daenerys Targaryen as a researcher concerned with the dragon species. The people of Westeros believed that dragons were decreasing in size due to captivity. Dragon size was normally measured as wingspan (meters) and captivity was normally measured in years. Daenerys used archival data and determined that the relationship between these two variables could be explained using the following regression equation: y-predicted = 453 - 2.5xInterpret this equation (i.e. What is its purpose? What is the intercept? What is the slope? What does it mean for dragons in Westeros?).
The owners of a chain of ice cream stores have the business objective of improving the forecast of daily sales so that staffing shortages can be minimized during the summer season. As a starting point, the owners decide to develop a simple linear regression model to predict daily sales based on atmospheric temperature. They select a sample of 15 consecutive days. The results are shown in the accompanying table. Complete parts (a) through (f) below. Click the icon to view the data table. E Click the icon to view a table of critical values of the Durbin-Watson statistic. a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b, and b,. b, = - 2.7630 (Round to four decimal places as needed.) %3D Ice cream sales b, = (Round to four decimal places as needed.) %3D Day Sales ($1,000) Temperature (°F) 63 1 2 1.52 1.68 71 75 3 1.92 1.79 74 76 4 2.02 2.36 6. 81 2.16 2.69 81 8 84 2.91 88 10 3.17 90 11 12 3.02 3.27 90 93 99 13 3.42 2.84 88 83 14 15…
The city wants to further develop the model to include the weather conditions of rainy, cloudy, or sunny. Ice Rink Attendance Temperature (°F) Weather Condition 140 45 Sunny 110 40 Cloudy 135 50 Cloudy 120 40 Cloudy 165 45 Sunny 180 45 Sunny 210 50 Sunny 190 45 Cloudy 170 40 Cloudy 130 45 Rainy 140 45 Cloudy 80 35 Rainy 120 45 Cloudy 100 45 Rainy What is the regression equation? Use the equation to forecast ice rink attendance if the temperature is 38°F and sunny. Should you keep weather condition in the model?
The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. Below is the data that represents the value (in $millions) and the annual revenue (in $millions) for 30 Major League Baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Team Revenue Value Baltimore 179 460 Boston 310 1000 Chicago White Sox 214 600 Cleveland 178 410 Detroit 217 478 Kansas City 161 354 Los Angeles Angels 226 656 Minnesota 213 510 New York Yankees 439 1850 Oakland 160 321 Seattle 210 585 Tampa Bay 161 323 Texas 233 674 Toronto 188 413 Arizona 186 447 Atlanta 203 508 Chicago Cubs 266 879 Cincinnati 185 424 Colorado 193 464 Houston 196 549 Los Angeles 230 1400 Miami 148 450 Milwaukee 195…
Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snel| "SA" (Sports Application) rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets (SoloRacer website). Helmet Weight (oz) Price ($) Pyrotect Pro Airflow 64 241 Pyrotect Pro Airflow Graphics 64 276 RCi Full Face 64 202 RaceQuip RidgeLine 64 197 HJC AR-10 58 291 HJC Si-12 47 708 HJC HX-10 49 910 Impact Racing Super Sport 59 331 Zamp FSA-1 66 197 Zamp RZ-2 58 292 Zamp RZ-2…
Please see problem with the solution: after reviewing the information below, assess the appropriateness and accuracy of using a linear regression model. Discuss the meaning of the standard error of the estimate and how it affects the predicted values of Y for that analysis. Many people are also using online shopping to avoid going to stores in person. I decided to use my own data. I am going to add how many Amazon transactions I have made each month from March- August. X= the month Y= amount of purchases Simple linear regression results: Dependent Variable: saleIndependent Variable: monthsale = 0.53333333 + 1.6 monthSample size: 6R (correlation coefficient) = 0.99410024R-sq = 0.98823529Estimate of error standard deviation: 0.36514837 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.53333333 0.50269117 ≠ 0 4 1.0609562 0.3485 Slope 1.6 0.087287156 ≠ 0 4 18.330303 <0.0001 Analysis of…
Show step by step on EXCEL. I am having a hard time on this.
The President of the Farmers Association wants to know how the amount of fertilizer and theamount of water given to plants affect their growth. The results were inputted into MINITABso as to fit the model. Regression Analysis: Growth versus Water, Fertilizer The regression equation isGrowth = ? + ? Water + ?Fertilizer Predictor Coef SE Coef T PConstant 42.085 ** 3.118 0.009Water 0.178 0.386 0.460 0.654Fertilizer 5.790 0.952 6.083 * S = 6.159 R-Sq = 77.1%% R-Sq(adj) = 73.3% Analysis of VarianceSource DF SS MS F PRegression 2 1532.603 766.301 *** ****Residual Error 12 455. 130 37.928Total 14 1987.733 iv Conduct a hypothesis test, at the 5% level of significance, to determine whether ? is…
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 99% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $818. The equation of the regression line is y = 1.451x - 40.698. Wages (state), x Wages (federal), y 713 760 785 805 851 870 921 926 947 985 1,002 1,045 1,091 1,145 1,185 1,239 1,281 1,307 1,320 1,400 Construct and interpret a 99% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $818. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. We can be 99% confident that when the average weekly wages of state government employees is $818, the average weekly wages of federal government employees will be between $ and…

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