You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N =(a) The estimated error variance 2=2.00. What is the sum of the squared least squares residuals?(b) The estimated variance of b₂ is 0.25, what is the standard error of b₂? What is the value of ✗(xi — ñ)²?-=52 observations.(c) Suppose the dependent variable y; is the state's mean income (in thousands of dollars) of males who are 18 years of age or older andpercentage of males 18 years or older who are high school graduates. Interpret the slope estimate 62 = 0.10.(d) Suppose=50.00 and y = 10.00, what is the estimate of the intercept parameter?(e) Given the results in (b) and (d), what is Σx??Ꮖ ;the(f) For the state of Arkansas the value of yiparts (c) and (d)).=12 and the value of xi = 60. Compute the least squares residual for Arkansas. (Hint: Use the information in

Step 1:Step 2:Step 3:The slope estimate b = 0.10 is interpreted as follows: for every 1% increase in…

Answered: You have the results of a simple linear…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆy=a+bxa=0.313b=0.145 (a) Write the equation of the Least Squares Regression line of the formˆy= + x(b) Which is a possible value for the correlation coefficient, r? -0.666 -1.772 1.772 0.666 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 4 years in a certain country, how much will the happiness index change? Round to two decimal places.Use the regression line to predict the happiness index of a country with a life expectancy of 65 years. Round to two decimal places.
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. A) Find the regression equation for predicting GPA from SAT scores. B) What percentage of the variance in GPAs is accounted for by the regression equation (i.e., compute the correlation, r, then find r2)? C) Does the regression equation account for a significant portion of the variance in GPA? Use a = .05 to evaluate the F-ratio.
What is the differed annual expenditures of two families if their annual net incomes are differed by 2000? The computed regression line has a value of a=4.32 and b=2.12.
9. A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation: foot length = 10.9+0.23- height One student in the sample was 73 inches tall with a foot length of 29 cm. What is the residual for this student? (а) 0 ст (b) 1.31 cm (c) 27.69 cm (d) 29 cm
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x, = distance traveled (miles) and x, = the number of deliveries made. Suppose that the model equation is Y = -0.800 + 0.060x, + 0.900x2 + € (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? 5.8 v hr (b) How would you interpret ß1 = 0.060, the coefficient of the predictor X1? o When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a…
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: ŷ=a+bx a=-0.523 b=0.177 (a) Write the equation of the Least Squares Regression line of the form j= 0.177 +| -0.523 (b) Which is a possible value for the correlation coefficient, r? O 1.936 O -0.632 O-1.936 O 0.632 (C) If a country increases its life expectancy, the happiness index will O decrease O increase (d) If the life expectancy is increased by 1 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 64 years. Round to two decimal places.
Two variables have the regression lines 3x + 2y = 26 and 6x + y = 31. Find the mean values, the correlation coefficient between x and y and the ratio of variances of the variables.
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: ý=a+bx a=-1.692 b=0.117 (a) Write the equation of the Least Squares Regression line of the form (b) Which is a possible value for the correlation coefficient, r? O -0.649 O 1.32 O 0.649 O-1.32 (c) If a country increases its life expectancy, the happiness index will O increase O decrease (d) If the life expectancy is increased by 2.5 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 75 years. Round to two decimal places.

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