Sophia Intro to Statistics Milestone 4

1:10 O b A O "Q. * a E (19 For numbers 1 to 3: The thermal condition in a cave is critical for sustaining a bat population. A sudden change in the temperature is related to deaths of bats in hundreds. An attempt to measure the degree of association between the temperature (in °C) and death toll (number of deaths) was done using 20 caves with reported cases of massive death among bats. Assume that temperature and death toll are bivariate normal. Given below is the R software output: > cor.test(temp , death) Pearson's product-moment correlation data: temp and death t - -1.4403, df - 148, p-value - 0.1519 alternative hypothesis: true correlation is not equal to e 95 percent confidence interval: -0.27269325 0.04351158 sample estimates: cor -0.1175698

This is a chart with Temperature Anomalies and Time, what does it indicate about global warming if  y = 0.0018x + 0.7418R² = 0.1015

ment Score: 85% O Attempt 2 on 1 of 14 > Each of the following graphs show the relationship between two variables. Determine the Pearson product-moment correlation coefficient (r) for each graph. 25- n 20- 15- 10- 5- 10 10 20 Variable I Variable I r= 0.0 r=-0.99 Answer Bank r=-0.99 r 0.0 r= -0.8 r= 0.9 r= 0.4 30- e 0.8- 0.6- 04- 10- r=-0.8 r= 0.4 02- 10 02 04 0.6 08 10 Variable Variable 1 DELL Variable 6 Variable 5

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Each of the following graphs show the relationship between two variables. Determine the Pearson product-moment correlation coefficient (r) for each graph

Calculate correlation coefficient from the following data : N= 10, E X= 140, E Y= 150 E (X – 10)2 = 180, E(Y– 15)² = 215, E (X- 10) (Y– 15) = 60 %3D %3D %3D %3D

10:07 AA www-awn.aleks.com O REGR. Predict. A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fifteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be î=-0.021 + 0.039.x. This line, along with a scatter plot of her data, is shown in Figure 1. Earnings per Current stock price, y (in dollars) share, x (in dollars) 30.62 0.89 15.77 0.47 40.14 1.88 51.19 1.61 25 26.79 1.06 18.54 0.74 59.71 2.26 20.78 0.75 38.96 1.16 34.97 1.44 41.67 0.98 42.69 1.43 32.30 1.81 58.49 2.74 Figure 1 29.83 1.44 Send data to Excel Based on her data and her regression line, answer the following: 1. Fill in the blank: For these…

A biologist is studying field mice particularly if there is a relationship between the caloric intake of a rat and its body mass. The caloric intake of rats varies with body mass as shown below. (Please refer to the photos attached) A. Find correlation coefficient (r), correct to 4 decimal places. B. Is there a linear correlation between these results? (Show scatter diagram) C. Determine the equation of regressuon line of caloric intake or body mass, expressing the alope and y- intercept. (Plot the estimated regression line on the scatter diagram) D. Estimate the caloric intake when the body mass is 4.8kg. (Show graph) 2. LINEAR CORRELATION & LINEAR REGRESSION PROBLEM A biologist is studying field mice particularly if there is a relationship between the caloric intake of a rat and its body mass. The caloric intake of rats varies with body mass as shown below. Body Mass kg (X) 3.4 3.6 4.6 5 | 7 8 8.5 9| 10 2 6 Caloric Intake, cal h-1 (Y) 1.5 2.1 3.2 3.6 3.6 3.9 4.1 4.2 4.5 4.6 5.9 A.…

5.2 The following table gives the vapor pressure of water for various temperatures. Temperature (°K) Vapor Pressure (mm Hg) 273 4.6 283 9.2 293 17.5 303 31.8 313 55.3 323 92.5 333 149.4 343 233.7 353 355.1 363 525.8 373 760.0 a. Plot a scatter diagram. Does it seem likely that a straight line model will be adequate?

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Class Size and Grades School administrators won- dered whether class size and grade achievement (in per- cent) were related. A random sample of classes revealed the following data. No. of students 15 10 8 20 18 6 Avg. grade (%) 85 90 82 80 84 92 Find y' when x = 12.

1:25 K The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below. Frequency A. 1852963O Relative Frequency O A. 4 7 10 13 16 Number of Customers (Type integers or decimals. Do not round.) (d) What percentage of the Saturdays had 10 or more customers waiting for a table at 6:00 P.M.? 0.6- 0.5- 0.4- 0.3- 0.2- 0.14 0- 14 7 10 13 16 Number of Customers (Type an integer or a decimal. Do not round.) (e) What percentage of the Saturdays had 12 or fewer customers waiting for a table at 6:00 P.M.? (Type an integer or a decimal. Do not round.) (f) Construct a frequency histogram of the data. Choose the correct histogram below. Frequency ||| B. = 18 15 12 Relative Frequency O B. Tralalalhulu! 1 4 7 10 13 16 Number of Customers 0.6- 0.5- 0.4- 0.3- 0.2 0.1- 0- 4 7 10 13 16 Number of Customers Frequency 9 11 10 13 8 Relative Frequency O 1852963 Vo) 1 LTE2 C. 8 10 (g) Construct a…

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approximately the same amount of wine per week. Here are the data (for drinkers only):" CANCER Wine intake x 2.5 8.5 15.5 26.5 (grams per day) Relative risk y 1.00 1.08 1.15 1.22 (a) Make a scatterplot of these data. Based on the scatter- plot, do you expect the correlation to be positive or negative? Near ±1 or not? (b) Find the correlation r between wine intake and relative risk. Do the data show that women who consume more wine tend to have higher relative risks of breast cancer? Wine and cancer in women. Some studies have suggested that a nightly glass of wine may not only take the edge off a day but also improve health. Is wine good for your health? A study of nearly 1.3 million middle-aged British women examined wine consumption and the risk of breast cancer. The researchers were interested in how risk changed as wine consumption increased. Risk is based on breast cancer rates in drinkers relative to breast cancer rates in nondrinkers in the study, with higher values indicating…

8.6 Husbands and wives, Part I. The Great Britain Office of Population Census and Surveys once collest data on a random sample of 170 married couples in Britain, recording the age (in years) and beich (converted here to inches) of the husbands and wives.° The scatterplot on the left shows the wife's plotted against her husband's age, and the plot on the right shows wife's height plotted against husbandie height. 70 65 40 20- 55- 40 60 60 65 70 75 20 Husband's age (in years) Husband's height (in inches) (a) Describe the relationship between husbands' and wives' ages. (b) Describe the relationship between husbands' and wives' heights. (c) Which plot shows a stronger correlation? Explain your reasoning. (d) Data on heights were originally collected in centimeters, and then converted to inches. Does this con- version affect the correlation between husbands' and wives' heights? Wife's age (in years) Wife's height (in inches)

Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (v). Summary quantities were 20 20 20 20 20 Σx 1478 , Σy- 12.75, Σ x-1432 15.8 , Σ.-8.86 and Σ xy 1083.67 n=1 n=1 n=1 n=1 n=1

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