SMAM 319 Exam1 Name 1. Pick the best choice. (10 points-2 each) _c A. A data set consisting of fifteen observations has the five number summary 4 11 12 13 15.5. For this data set it is definitely true that. a. It does not have any outliers. b. The number 4 is the only outlier. c. The data set has at least one outlier. d. The data set has more than one outlier. e. The number 15 is an outlier. a B.The equation of a line is 3x + y =6. The slope is a. -3 b.3 c.6 d.1/3 e.-1/3 _c C. The grades on an examination are normally distributed. The Z scores are calculated. According to the empirical rule a. at least 89% of the Z scores of the data points are between -3 and 3 b. at most 25% of the Z scores are greater than 2 c. about 69% of the Z scores are between 1 and 1 d. about 95% of the Z scores are between 3 and 3 e. at most 10 % of the Z scores are less than -3. c D. Two variables x and y are positively correlated. This means that a. The slope of the regression line is negative. b. As x increases y decreases. c. As x increases y increases. d. There is no association between the variables. e. A straight line is the best model. _d E. A correlation coefficient of 0.12 means that a. there is a weak positive association between two variables b.there is a strong positive association between two variables c. the regression line has a positive slope d. there is a weak negative association between two variables e. there is a strong negative association between the two variables. 2. A. Find the equation of the line that connects the points ( 1,2) and (1,6).(10 points) m = 6! 2 1! (!1) = 2 y! 2 = 2(x +1) y! 2 = 2x + 2 y = 2x + 4 B. What is the slope and the y intercept? (5 points) Slope =2 Yintercept =4
3. The data below represents the number of home runs hit by Mark Mc Gwire during 16 different seasons from lowest to highest. 3 29 39 52 9 32 39 58 9 32 42 65 22 33 49 70 A. Make a stem and leaf display.(4 points) 0 3 9 9 1 2 2 9 3 2 2 3 9 9 4 2 9 5 2 8 6 5 7 0 B. Make a five number summary.(5 points) 36 25.5 50.5 3 70 36 23.75 51.25 3 70 C. What are the outliers if any. (2 points) There are no outliers.
D. Draw a boxplot (5 points) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 E. Comment on the shape of the data. Is it bell shaped skewed to the right or left? Explain. (4 points) The data appears to be slightly skewed toward the right. 4. The average heights of a large group of people has a mean of 69 inches and a standard deviation of 5 inches. A. What is the Z score of a person whose height is 72 inches?(5 points) Z = 72! 69 5 =.6 B. Using Chebychev Theorem at least what percentage of the heights is between 61 and 77 inches? (5 points) 8=5k k=1.6 1!1/ (1.6) 2 =.609 60.9% C. Suppose the heights are normally distributed. Between what two limits would you expect to find about 69% of the heights? (5 points) 64 and 74 one standard deviation either way. 5. The weights in pounds of eight vehicles and the variability of their braking distances when stopping on a wet surface Weight, x 5720 4050 6130 5000 5010 4270 5500 5550 Variability in braking distance, y 3.78 2.43 4.63 2.88 3.25 2.76 3.42 3.51 Fit the regression line using your calculator. Fill in the blanks.
A. The equation of the regression line is _y=.0008915x - 1.262 (2 points) B. The slope is_.0008915 and the Y intercept is -1.262 (4 points) C. The percentage of variation accounted for by the regression line is 87.1 (2 points) The correlation coefficient is.934 (2 points) D. How much variability in feet does a 6000 lb car have? (4 points) Y=.0008915(6000)-1.262=4.087 E. Would a heavier car have a larger or a smaller variability than a lighter car? Explain your answer on the basis of the results in A-C. (4 points) A heavier car would have a larger variability than a smaller car.the slope and the correlation coefficient are positive so as weight increases so does variability. 6.Classified ads in the Ithaca Journal offered several used Toyota Corrllas for sale during 2007. Listed below are the ages of the cars and the advertised prices. Row Age(x) Price(y) 1 1 13990 2 1 13495 3 3 12999 4 4 9500 5 4 10495 6 5 8995 7 5 9495 8 6 6999 9 7 6950 10 7 7850 11 8 6999 12 8 5995 Consider the scatterplot below
Based only on the above scatterplot. A. Does the data appear to be positively or negatively correlated? Explain. (2 points) The data is negatively correlated. As x increases y decreases. B. Would it appear that a straight line model is appropriate? Explain. (2 points) Yes a straight line model probably would be appropriate. The points lie close to a straight line. Consider the Minitab output below. Regression Analysis: Price(y) versus Age(x) The regression equation is Price(y) = 14286-959 Age(x) Predictor Coef SE Coef T P Constant 14285.9 448.7 31.84 0.000 Age(x) -959.05 64.58-14.85 0.000 S = 816.214 R-Sq = 94.4% R-Sq(adj) = 94.0% Analysis of Variance Source DF SS MS F P Regression 1 146917777 146917777 220.53 0.000
Residual Error 13 8660659 666205 Total 14 155578436 Unusual Observations Obs Age(x) Price(y) Fit SE Fit Residual St Resid 3 3.0 12999 11409 292 1590 2.09R R denotes an observation with a large standardized residual. A. What is the equation of the regression line?(2 points) Y=14285.9-959.05x B. What percentage of the variation is accounted for by the regression line?(2 points) Thre regression line accounts for 94.4% of the variation. C. What is the correlation coefficient?(4 points) The correlation coefficient is -.9715 D. What is the residual when x = 3, y=12999? (6 points) Y pred = 14285.9 959.05(3)=11408.75 Yobs = 12999 Y obs Ypred = 12999-11408.75=1590.25 E. Based on the scatterplot, the correlation coefficent and the percentage of the variation of the regression model write a paragraph about the adequacy of the model?(5 points) This appears to be a very adequate model. The points on the scatterplot lie very close to a straight line. The regression line accounts for 94.4% of the variation and the correlation coefficient is -.9715 close to -1. There is a strong negative linear relationship between the two variables. G. Does it appear that older cars cost less money based on the regression line? Explain.(5 points) Based on the regression line older cars cost less money. The slope and the correlation coefficient is negative so as age increases cost decreases.