You are assisting the county assessor (whose job is to assess the value of properties for property tax purposes) in determining a model where the price of a single-family residential property in a given neighborhood can be predicted based on the size of the property (square feet). You obtain a sample of residential properties. You run a regression and obtain the following regression output from Microsoft Excel. y = PRICE x = SQFT Square feet Regression Statistics Multiple R 0.4404 R Square Adjusted R Square 0.1931 Standard Error Observations 1000 ANOVA df SS MS F Significance F Regression 1 586664.2 240.08 1.1E-48 Residual 998 2438732.6 Total 999 3025397 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 126.3042 11.1587 11.3189 0.0000 104.4069 148.2014 SOFT 0.0676 1.1E-48

You are assisting the county assessor (whose job is to assess the value of properties for property tax purposes) in determining a model where the price of a single-family residential property in a given neighborhood can be predicted based on the size of the property (square feet). You obtain a sample of residential properties. You run a regression and obtain the following regression output from Microsoft Excel. y = PRICE x = SQFT Square feet Regression Statistics Multiple R 0.4404 R Square Adjusted R Square 0.1931 Standard Error Observations 1000 ANOVA df SS MS F Significance F Regression 1 586664.2 240.08 1.1E-48 Residual 998 2438732.6 Total 999 3025397 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 126.3042 11.1587 11.3189 0.0000 104.4069 148.2014 SOFT 0.0676 1.1E-48

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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?
Question 25: Based on the data shown below, calculate the regression line (each value to two decimal places)y = x + x y 1 33.46 2 31.94 3 29.42 4 27.5 5 24.78 6 21.76 7 22.64 8 20.22 9 16.9 10 16.58 11 11.26 12 9.24 13 8.22 14 7.2
Question 4 The following table displays the mathematics test scores for a random sample of college students, along with their final SY16C grades. Fit the regression line y = a+bx to the data and interpret the results. Use the regression equation to determine the SY16C grade for a college student who scored 60 on their achievement test. What would their SY16C grade be? Mathematics test (x) SY16C grades (y) 1 39 65 2 43 78 3 21 52 4 64 82 5 57 92 6 47 89 7 28 73 8 75 98 9 34 56
Question 23: Based on the data shown below, calculate the regression line (each value to at least two decimal places)y = x + x y 1 9.55 2 9.62 3 6.99 4 8.76 5 7.33 6 4.1
Question 5 Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel. Revenue People Income Competitors Price Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027 Sample…
Use the dataset in Table 2 to answer the questions. The table shows the ages (in years) of seven children and the number of words in their vocabulary. For problems 9-12, use the regression equation found in question 7 to predict the value of for the values of given in each question unless it is not meaningful. If it is not meaningful to predict the value of for the -value, explain why not. Table 2. Vocabulary Age Vocabulary 3 1100 4 1300 4 1500 5 2100 6 2600 2 460 3 1200 7. What is the equation of the regression line? 8. Construct a scatter plot for the data showing the regression line on the same graph. For problems 9-12, see the instructions above. 9. x=2years 10. x=3years 11. x=6years 12. x=12years
Question #9 Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 400metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports 233 269 364 492 548 Crash Fatality Rate 15.9 15.7 15.4 15.4 15 Find the equation of the regression line. y= ___________+( __________ ) x (Round the y-intercept to three decimal places as needed. Round the slope to four decimal places as needed.) The best predicted crash fatality rate for a year in which there are 400 metric tons of lemon imports is _________fatalities per 100,000 population. (Round to one decimal place as needed.) Is the prediction worthwhile? A. Since all of the requirements for finding the equation of the regression line are…
QUESTION 13 Below is some of the regression output from a regression of the amount various customers paid for a new car (expressed in dollars) versus the age of the customer (expressed in years), the number of previous cars the customer had purchased from the dealership in the past, a dummy variable indicating the gender of the customer (=1 for a Man and = 0 for a woman), and an interactive term the multiplies the age of the customer with the gender dummy variable. Regression Statistics Multiple R 0.963 R Square Adjusted R Square Standard Error Observations 20 ANOVA df SS MS F Significance F Regression 24686354.49 6171589 47.8 2.3289E-08 Residual 129243 Total 26625000…
Question 2 The following regression output was obtained. The regression model is Test scores onstudent teacher ratio. When your research assistant cut and pasted the results for you, therewere several vital pieces of information missing. See output below: SUMMARYOUTPUTRegression StatisticsMultiple R 0.226362751R Square (a)Adjusted R Square 0.048970335Standard Error 18.5809675Observations 420ANOVA df SS MS FRegression 1 7794.110041 7794.110041 22.57511055Residual 418 144315.4836 345.2523531Total 419 (b) Coefficients Standard Error t Stat P-valueIntercept 698.9329523 9.467491444str -2.279808287…
Question 2 The following regression output was obtained. The regression model is Test scores onstudent teacher ratio. When your research assistant cut and pasted the results for you, therewere several vital pieces of information missing. See output below: SUMMARYOUTPUTRegression StatisticsMultiple R 0.226362751R Square (a)Adjusted R Square 0.048970335Standard Error 18.5809675Observations 420ANOVA df SS MS FRegression 1 7794.110041 7794.110041 22.57511055Residual 418 144315.4836 345.2523531Total 419 (b) Coefficients Standard Error t Stat P-valueIntercept 698.9329523 9.467491444str -2.279808287…

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30	The following figure computed from SQFT data is given:	∑(? − ?̅)² =	128237398.86
	Find standard error of the slope coefficient, se(?₁) = ______.
	The margin of error to build a 95% confidence interval for the slope coefficient that relates the price response to each additional square foot is _______.

a	0.005
b	0.009
c	0.016
d	0.028