Question

Question 11 B0/2 pts 3 Detalls Consider the following data set that contains information about a sample of ten 2015 Honda Accord offered for sale Vehicle Condition Color 100miles 1000) Mileage Price 1 average green 19 2 good blue 29 3 good silver 33 28 4 poor red 39 27 5 green 26 6 good silver 25 7 excellent green 24 8 poor black 46 23 9 good white 22 10 good blue 21 The scatter plot that summarizes the data with regard to mileage as the input variable and price as the output variable is provided below. good a. Is there an association between the two variables? If yes, is it positive or negative? There appears to be Betech narave between the two variables. b. Use technology to find the equation of the line of best fit, y = mx + 6, and the coefficient of determination and interpret the slope, the vertical intercept, and the coefficient of determination (Round the answers to 3 decimal places.) Select name m. b = Select hence there is a Sector linear relation c. Use the line of best fit to: 1. estimate the price of a car with 30500 miles. Answer: dollars (Round the answer to the nearest unit.) il. estimate the mileage of a car whose price is 27500 dollars Answer: miles (Round the answer to the

Answer 1

a) As the mileage increases, the price of the vehicle decreases. Hence, we can say that there is a negative relation between the two variables b) As Price is the output variable, it is the dependent variable (y) and mileage is the independent variable (x) Vehicle Price ($'1000) Mileage(1000miles) 1 30 19 2 29 29 3 28 33 27 39 5 26 42 6 25 43 7 24 45 8 23 46 9 22 62 10 21 67 4 We are using Excel's Regression tool available under Data Analysis. Regression X ? Input OK Input Y Range: $C$2:$C$121 1 Cancel Input X Range: $D$2:$D$12 1 Help Constant is Zero Labels confidence Level: 95 % Output options Output Range: New Worksheet bly New Workbook Residuals Residuals Standardized Residuals Residual plots Line Fit Plots Normal Probability Normal Probability Plots Set the parameters as mentioned above. The results look like:

SUMMARY OUTPUT Regression Statistics Multiple R 0.959551228 R Square 0.920738559 Adjusted R Square 0.910830879 Standard Error 0.9040927 Observations 10 ANOVA dr Significance F 1.11522E-05 1 Regression Residual Total SS 75.96093112 6.539068881 82.5 MS F 75.96093112 92.93180115 0.81738361 8 9 Coefficients Standard Error t Stat p-value Lower 95% Upper 9596 Lower 95.0% Upper 95.0% Intercept 34.14347944 0.941094255 36.28061617 3.65045E-10 31.9733122 36.31364669 31.9733122 36.31364669 Mileage(1000miles) -0.203375987 0.021096844 -9.640114167 1.11522E-05 -0.252025397 -0.154726577 -0.252025397 -0.154726577 Hence, the equation is given as Y = mx + b i. ii. Price = -0.20338*Mileage + 34.14348 m=-0.20338 is the slope b = 34.14348 is the vertical intercept r = 0.92074 (as denoted by R square value above). As the value is close to 1, hence there is a strong linear relation iii. c) Price = -0.20338*Mileage +34.14348 i. Mileage = 30500 miles or 30.5 as per our equation Price = -0.20338*30.5 + 34.14348 = 27.94039 Hence the price of this car should be 27.94039*1000 = $27,940 ii. Price = $27,500 or 27.5 as per our equation 27.5 = -0.20338*Mileage + 34.14348 Mileage = 32.6653 Hence the mileage of this car should be 32.6653*1000 = 32,665 miles