The following are the weight (in grams) and quantity of volatile emissions (in hundreds of nanograms) for plants. A scatterplot of the data is given to the right. Weight (x) 57 86 55 67 52 67 61 79 79 54 8.5 22.0 10.0 22.0 12.0 11.0 7.0 13.5 16.5 22.0 Quantity (y) 30- 20-4 10+ a. r= (Round to three decimal places as needed.) 40 60 80 100 a. Obtain the linear correlation coefficient. b. Interpret the value of r in terms of the linear relationship between the two variables. c. Discuss the graphical interpretation of the value of r. d. Obtain the value of the coefficient of determination by squaring r.

An investigation of the properties of bricks used to line aluminum smelter pots was published in an article. Six different commercial bricks were evaluated. The life span of a smelter pot depends on the porosity of the brick lining (the less porosity, the longer the life span); consequently, the researchers measured the apparent porosity of each brick specimen, as well as the mean pore diameter of each brick. See the table. Apparent Porosity (y). Mean Pore Diameter (x). Click the icon to view the table. Data table Mean Pore Diameter Apparent Porosity (%) (micrometers) Brick Interpret the y-intercept of the line. Choose the correct answer below. 18.7 12.0 В 18.3 9.8 O A. The y-intercept is Bo- This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter. 16.3 7.3 6.9 5.4 O B. The y-intercept is Bo: For each unit increase in mean pore diameter, the mean porosity is estimated to increase by B0- 17.2 10.9 O C. There is not enough…

aChen -. M Gmail YouTube Maps oscar - Google D... Translate New Tab ece Gler 2/6 100% SID: 2. A researcher is studying the relationship between various properties of wine and their taste characteristics. The histogram below shows the amount of residual sugar (sugar left after fermentation) in a collection of wines. However, one of the bars, between 3 and 5 grams per liter, is missing. 50 (47.9) (38.7) 30 10 (0.1) (0.92) (0.1) 2 10 15 Residual sugar (grams/liter) Calculate the height of the missing bar and draw it in. (Show your work below, and indicate the numerical value in parentheses above the bar.) % per gramlter

Suppose the correlation between height and weight for adults is +0.80. What proportion of the variability in weight can be explained by the relationship with height? A. 20% B. 36% C. 64% D. 80%

Assume the correlation coefficient between advertising dollars spent and sales is .78. How much of the variability in sales is explained by the relationship between sales and advertising dollars? a. 39.16% b. 60.84% c. 78% d. 22%

The following table gives the weeks of gestation and corresponding birth weights for a sample of 5 babies. Weeks of Gestation    Weight (in pounds)34    4.535    636    737    8.538    9.5 Step 3 of 3 :  Calculate the coefficient of determination, r2 Round your answer to three decimal places.

Which of the following is the most appropriate equation to model the data?  ŷ = –10.89x + 0.85  ŷ = –0.85x + 10.89  ŷ = 10.89(0.85)x  ŷ = 0.85(10.89)x

The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temperatures are in the following table: Usage/ Month Temp. 1000 Month 21 185.79 July. 24 214.47 Aug. 32 288.03 Sept. 47 424.84 Oct. 50 454.58 Nov. 59 539.03 Dec. Jan. Feb. Mar. Apr. May June Temp. 68 74 62 50 41 30 Identify which are the independent and dependent variables. Usage/ 1000 621.55 675.06 562.03 452.93 369.95 273.98

For the following example indicate the type of data involved using the following: A = nominal data B = ordinal data C = interval data 1. Number of patients with coronary pathology in nursing homes in the U.S

Q1. A study was conducted to investigate the relationship between premature birth and mental development at 12 months. The infant's birth weight was used as an index of prematurity. At age 12 months, the child's mental development was recorded. The results are shown below (the weights are in pounds): Birth 4 6 7 8 Weight(x) Developmental 85 Quotients(y) 88 87 94 96 Summary: n = 5, £x=30, £x² = 190, Ey= 450, Ey² = 40590, Exy = 2728 . a. Find the least square prediction equation, y on x. b. Obtain a 95% confidence interval for the average value of y when x 6.5 (i.e., a C.I. for E(y|x= 6.5)). c. Obtain the coefficient of correlation (r) and interpret the result. d. Test the hypothesis that H, :p= 0 vs. H, : p0. Use a =0.05.