11.21 Consider the following pairs of measurements. D L11021 x y 54 5 4 33 3 -1 2 7 3 0 1 8 65 5 43 3 a. Construct a scatterplot of these data. b. What does the scatterplot suggest about the relation- ship between x and y? xx c. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286, and 3.7143, calculate the least squares estimates of Bo and B. 020; .918 d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain. e. Interpret the y-intercept and slope of the least squares line. Over what range of x are these interpretations meaningful?

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.8333, sx = 2.0412, y = 4.3167, sy = 1.3363, and r= -0.9153, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). X y 1 2 4 4 5.4 5.9 5.0 4.0 (a) Choose the correct graph below. O A. Q Q 2 B. There appears to be a linear, negative relationship. (b) y = -0.599 x + (6.614) (Round to three decimal places as needed.) (c) Choose the correct graph below. 6 6 2.6 3.0 B. Q Q L Q C. Q L D. Q Q L Q

A data set is given below.   ​(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ​(b) Given that x=3.8333​, sx=2.4014​, y=3.6500​, sy=1.7942​, and r=−0.9539​, determine the​ least-squares regression line. ​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a).

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.8333, sx = 2.0412, y = 3.8833, sy = 1.5651, and r= -0.9338, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). X y O A. 1 2 4 4 6 5.2 5.8 4.5 3.6 2.0 (a) Choose the correct graph below. Q 6 6 2.2 D There appears to be a linear, negative relationship. (b) y = x + ( (Round to three decimal places as needed.) B. 6- 0 Y ← O C. 6- 0 .. O D. Ay 67 0-

A data set is given below.   ​(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ​(b) Given that x=3.6667​, sx=2.3381​, y=4.5833​, sy=1.6376​, and r=−0.9315​, determine the​ least-squares regression line. ​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a).   x 1 1 3 5 6 6   y 5.4 6.8 5.8 3.6 2.8 3.1

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.8333, sy = 2.4014, y = 4.0500, sy = 1.5997, and r= - 0.9345, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 2 4 6. y 5.8 5.8 4.7 3.2 2.2 2.6 (a) Choose the correct graph below. O A. O B. C. Ay 6- Ay 6- Ay 6- 6- X X 0- 0- 0- 6. 6 6. There appears to be a linear, negative relationship. (b) y =x+ (O %3D (Round to three decimal places as needed.)

Consider the following pairs of measurements: a. Use Stata to chart a scattergram for the data. Show the graph below. X 5 8 3 4 9 Y 6.2 3.4 7.5 8.1 3.2   b. Use Stata to estimate the least squares model between X and Y. Copy the output below and specify the least squares equation. c. What are SSE, s2, and s?

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sx =2.4221, y = 3.8667, sy = 1.8435, andr= -0.9525, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). D O A. (a) Choose the correct graph below. Ay 6- X y 0 0 2 3 5 6 6 5.8 5.7 5.0 2.8 1.7 2.2 O G B. Ay 6- Q (...) C. 0- ● Q D. Ау 0- X 6

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sy =2.3381, y = 3.9167, s, = 1.8563, and r= - (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 0.9570, determine the least-squares regression line. 1 1 y 5.1 6.4 5.1 2.8 1.9 2.2 (a) Choose the correct graph below. O A. В. Ay 7- Ay 7- Ay 7- X X 6 6 6. There appears to be a linear, negative relationship. (b) y =x+ (O (Round to three decimal places as needed.)

Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows. Age Number of Driver Deaths per 100,000 17.5 38 22 36 29.5 24 44.5 20 64.5 18 80 28 a. Calculate the least squares (best-fit) line. Put the equation in the form of: ý = a+ bx. ý = 35.582+-.192x For each age group, pick the midpoint of the interval for the x value. (For the 80+ group, use 85. Enter exact numbers as integers, fractions, or decimals.) i. Age Group Midpoint 15-24 25-39 40-69 70-79 80+ Predict the number of deaths for age 26. (Use your equation from part (a). Round your answer to one decimal place.) ii. deaths per 100,000 Predict the number of deaths for age 60. (Use your equation from part (a). Round your answer to one decimal place.) iii. deaths per 100,000