An economist is interested in predicting the GDP per capita in Afghanistan based on Algeria. He has data from 2012-2019. Find the least-squares regression equation. year Afghanistan Algeria 2012 1770 13200 2013 1810 13300 2014 1800 13500 2015 1770 13800 2016 1760 13900 2017 1760 13900 2018 1740 13900 2019 1760 14000 O yhat= 59624.1-27.25x O yhat= 2485-0.052x O yhat= -59624.1 +27.25x Oyhat= -2485 +0.052x
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- Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53According to an article, one may be able to predict an individual's level of support for ecology based on demographic and ideological characteristics. The multiple regression model proposed by the authors was the following. y = 3.60-.01x₁+.01.₂-.07x3+.12x4+.02xs-.04x6-01-.04.xg-.02.xg+c The variables are defined as follows. y = ecology score (higher values indicate a greater concern for ecology) X₁ = age times 10 x₂ = income (in thousands of dollars) x3 = gender (1 = male, 0 = female) X4 = race (1 = white, 0 = nonwhite) X5 = education (in years) x6 = ideology (4 = conservative, 3 = right of center, 2 = middle of the road, 1 = left of center, and 0 = liberal) X7 = social class (4 = upper, 3 = upper middle, 2 = middle, 1 = lower middle, 0 = lower) xg = postmaterialist (1 if postmaterialist, 0 otherwise) x9 = materialist (1 if materialist, 0 otherwise) (a) Suppose you knew a person with the following characteristics: a 30 year old, white female with a college degree (20 years of…A new footwear manufacturer is trying to compete with the major brands by investing heavily in Research and Development (R&D). Their goal is to produce a premium lifestyle sneaker that is more comfortable, longer lasting and more stylish than any of their competitors. Below are some data on dollars spent on R&D and new customers acquired for the last 5 quarters. Regression Equation: Y= 0.5 + 1.35X New Customers R&D Dollars Acquired (in millions) (in thousands) 8 12 12 15 13 18 14 20 18 25 Based on looking at the numbers and/or sketching a scatter-plot, what conclusion can we draw about the data? The variables are negatively correlated You cannot tell until we perform some calculations There does not appear to be a strong correlation between the variables The variables are positively correlated
- The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The following data represents the value in 2014 (in $millions) and the annual revenue (in $millions) for the 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 245 1000 Boston 370 2100 Chicago White Sox 227 975 Cleveland 207 825 Detroit 254 1125 Houston 175 800 Kansas City 231 700 Los Angeles Angels 304 1300 Minnesota 223 895 New York Yankees 508 3200 Oakland 202 725 Seattle 250 1100 Tampa Bay 188 625 Texas 266 1220 Toronto 226 870 Arizona 211 840 Atlanta 267 1150 Chicago Cubs 302 1800 Cincinnati 227 885 Colorado…Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:The table lists the average tuition and fees at private colleges and universities for selected years. Year 1985 1990 1995 2000 2008 5311 25,115 Tuition and Fees (in dollars) 9375 SO 12,418 (a) Find the equation of the least-squares regression line that models the data. y 840.450 (Type the slope as a decimal rounded to three decimal places. Round the y-intercept to the nearest integer.) (b) Graph the data and the regression line in the same viewing window using the parameters given below the graph choices. Choose the correct graph below. OA. O B. o HE RO OC. 16,230 A o ƠN
- We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation information at the firm-level. We are interested in predicting a company's sales based on the CEO's salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to estimate the linear regression sales; = a + ßsalary; + ei and get the following regression results: . regress sales salary Source Model Residual Total sales salary cons SS 337920405 2.3180e+10 2.3518e+10 df 1 207 208 Coef. Std. Err. .9287785 .5346574 5733.917 1002.477 MS 337920405 111980203 113066454 Number of obs F (1, 207) Prob > F R-squared t P>|t| = Adj R-squared = Root MSE 1.74 0.084 5.72 0.000 = = -.1252934 3757.543 = 209 3.02 0.0838 0.0144 0.0096 10582 [95% Conf. Interval] 1.98285 7710.291 This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary. Interpret the…Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion. In particular, note the variables Barefoot and Footwear2. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear2 represents their range of ankle motion (in degrees) while wearing medical shoes. Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing medical shoes, ?̂ , based on their range of ankle motion while barefoot, ? . Round your coefficients to two decimal places of precision. ?̂ = A physical therapist determines that her patient Jan has a range of ankle motion of 7.26°7.26° while barefoot. Predict Jan's range of ankle motion while wearing medical shoes, ?̂ . Round your answer to two decimal places. ?̂ = Suppose Jan's…A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…
- According to an article, one may be able to predict an individual's level of support for ecology based on demographic and ideological characteristics. The multiple regression model proposed by the authors was the following. y = 3.60-.01.x₁ +.01.x2-.07x3+.12x4+.02xs-.04x6-.01x7.04x8-.02xg+e The variables are defined as follows. y = ecology score (higher values indicate a greater concern for ecology) x₁ = age times 10 x₂ = income (in thousands of dollars) x3 = gender (1 = male, 0 = female) X4 = race (1 = white, 0 = nonwhite) X5 = education (in years) x6 = ideology (4 = conservative, 3 = right of center, 2 = middle of the road, 1 = left of center, and 0 = liberal) X7 = social class (4 = upper, 3 = upper middle, 2 = middle, 1 = lower middle, 0 = lower) x8 = postmaterialist (1 if postmaterialist, 0 otherwise) x9 = materialist (1 if materialist, O otherwise) (a) Suppose you knew a person with the following characteristics: a 30 year old, white female with a college degree (20 years of…Five students took an aptitude test prior to their algebra course. What linear regression equation best predicts algebra performance, based on aptitude scores? If a student made an 80 on the aptitude test, what grade would we expect her to make in algebra? How well does the regression equation fit the data? Student aptitude test algebra grade 1 95 85 2 85 95 3 80 70 4 70 65 5 60 70Linear regression is a highly effective data analysis method that accurately estimates the value of unknown data using related and known data. This is achieved using a linear equation that accurately models the quantitative relationship between the dependent (unknown) and independent (known) variables. In other words, by looking at how one variable affects another, this method can accurately forecast the value of the dependent variable. It involves choosing the variable to forecast and using another variable to make informed predictions about its value. In experiments, the independent variable is the cause, and its value remains constant while other variables have been modified. On the other hand, the dependent variable is the effect, and changes influence its value in the independent variable. As I began my business, I struggled with determining the appropriate pricing for my products. It was important that the prices were reasonable while allowing for a profit. The pricing had to…