1.The accompanying data was read from a graph. The independent variable is SO₂ deposition rate (mg/m²/d) and the dependent variable is steel weight loss (g/m²).

x	15	18	33	43	45	118
y	270	350	480	500	560	1160

(b) Calculate the equation of the estimated regression line. (Round all numerical values to two decimal places.) y=

(c) What percentage of observed variation in steel weight loss can be attributed to the model relationship in combination with variation in deposition rate? (Round your answer to one decimal place.) % (d) Because the largestxvalue in the sample greatly exceeds the others, this observation may have been very influential in determining the equation of the line. Delete this observation and recalculate the equation. (Round all numerical values to two decimal places.) y* =

2.The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in an article.

x	1.2	1.4	1.5	2.0	2.1	2.7	2.7	2.7	2.8	2.9	3.0	3.5	3.8	3.8	4.5	5.1	5.7
y	15	3	31	1	13	0	8	15	2	1	7	35	25	10	35	58	56

Summary quantities include

S_xx = 25.6506,

S_yy = 5546.2353,

and

S_xy = 265.1882.

(a)Calculate the value of the sample correlation coefficient. (Round your answer to three decimal places.)Interpret the value of the sample correlation coefficient.

.(b)If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship? (Round your answer to three decimal places.)(c)If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship? (Round your answer to three decimal places.)(d)Carry out a test of

H₀: = 0.5

versus

H_a: > 0.5

using a significance level of 0.05. [Note: The article reported the P-value for testing

H₀: = 0

versus

H₀: 0.]

(Round your test statistic to two decimal places and your P-value to four decimal places.)z=P-value=

3.The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and muscular endurance y. The accompanying data was read from a plot in the paper.

x	410	760	780	810	840	1,035	1,190	1,260	1,290	1,390	1,465	1,490	1,515	2,210
y	3.90	3.90	4.80	5.10	4.10	3.40	6.40	6.78	7.65	4.85	7.90	4.35	6.50	8.80

S_xx = 2,615,573.214, S_yy = 38.4598, S_xy = 7,393.061. A scatter plot shows a linear pattern.

a.Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.)r = b.Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t	=
P-value	=

(c)If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)

d.If a regression analysis were to be carried out to predict lactate level from endurance, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.

4. The following data is representative of that reported in an article on nitrogen emissions, withx= burner area liberation rate (MBtu/hr-ft²) andy= NO_xemission rate (ppm):

x	100	125	125	150	150	200	200	250	250	300	300	350	400	400
y	140	130	170	220	190	330	290	390	440	440	380	590	600	660

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.) y=

(b) What is the estimate of expected NO_xemission rate when burner area liberation rate equals205? (Round your answer to two decimal places.) ppm (c) Estimate the amount by which you expect NO_xemission rate to change when burner area liberation rate is decreased by60. (Round your answer to two decimal places.) ppm

5.For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:

x	112.3	97.0	92.7	86.0	102.0	99.2	95.8	103.5	89.0	86.7
y	74.5	70.7	57.8	48.7	74.5	73.3	67.9	59.2	57.7	48.3

(a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) y=

(b) Calculate the coefficient of determination. (Round your answer to four decimal places.) (c) Calculate an estimate of the error standard deviationin the simple linear regression model. (Round your answer to three decimal places.) MPa

6.An article gave a scatter plot along with the least squares line ofx= rainfall volume (m³) andy= runoffvolume (m³) for a particular location. The accompanying values were read from the plot.

x	7	12	14	20	23	30	40	51	55	67	72	82	96	112	127
y	4	10	13	15	15	25	27	46	38	46	53	74	82	99	100

(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.)

slope
intercept

(c) Calculate a point estimate of the true average runoff volume when rainfall volume is54. (Round your answer to four decimal places.) m³ (d) Calculate a point estimate of the standard deviation. (Round your answer to two decimal places.) m³ (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)

7.A statistical program is recommended.Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. An article reported data on ranges in maximum inclination angles of the head in the clockwise anterior, posterior, right, and left directions for 14 randomly selected subjects. Consider the accompanying data on average anterior maximum inclination angle (AMIA) both in the clockwise direction and in the counterclockwise direction.

Subj:	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Clockwise (Cl):	57.9	35.7	54.5	55.8	51.1	70.8	77.3	51.6	54.7	63.6	59.2	59.2	55.8	38.5
Counterclockwise (Co):	44.2	52.1	60.2	51.7	47.2	65.6	71.4	48.8	53.1	66.3	59.8	47.5	64.5	34.5

(a)Calculate a point estimate of the population correlation coefficient between Cl AMIA and Co AMIA

Cl =785.7,

Co =766.9,

Cl²=45,614.71,

Co²=43,373.67,

ClCo =44,079.37.

Round your answer to three decimal places.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)t=P-value=