Question

Data:

Bob wishes to study the relationship between mean annual temperature (Temp) and the mortality rate (SMI) for a type of breast cancer in women at a 5% significance level and collects paired sample data.

SMI   100   96   95   89   89   79   82   72   65   68   53
Temp   50   49   48   47   45   46   44   43   42   40   34

1) Determine predictor variable, x, and response variable, y. What is the response variable?

Group of answer choices

A) y=mean annual temperature (Temp)

B) y=mortality rate (SMI) for a type of breast cancer in women

C) x=mean annual temperature (Temp)

D) x=mortality rate (SMI) for a type of breast cancer in women

2)Calculate r (rounded to the nearest ten-thousandth).

3)Is there sufficient evidence support the claim of linear correlation? Why? (Hint: Complete a linear correlation hypothesis test using Table A-6.)

Group of answer choices

A) There is sufficient evidence to support the claim of linear correlation because the absolute value of r is larger than the critical value from Table A-6 of 0.602.

B) There is not sufficient evidence to support the claim of linear correlation because the absolute value of r is larger than the critical value from Table A-6 of 0.602.

C)There is sufficient evidence to support the claim of linear correlation because the absolute value of r is not larger than the critical value from Table A-6 of 0.735.

D) There is not sufficient evidence to support the claim of linear correlation because the absolute value of r is larger than the critical value from Table A-6 of 0.735.

E) There is sufficient evidence to support the claim of linear correlation because the absolute value of r is not larger than the critical value from Table A-6 of 0.602.

F) There is sufficient evidence to support the claim of linear correlation because the absolute value of r is larger than the critical value from Table A-6 of 0.735.

G) There is not sufficient evidence to support the claim of linear correlation because the absolute value of r is not larger than the critical value from Table A-6 of 0.602.

H) There is not sufficient evidence to support the claim of linear correlation because the absolute value of r is not larger than the critical value from Table A-6 of 0.735.

4)Find the slope of the regression line (rounded to the nearest ten-thousandth).

5)Find the y-intercept of the regression line (rounded to the nearest ten-thousandth).

6) Calculate the best point estimate for the mortality rate (SMI) for a type of breast cancer in women at mean annual temperature (Temp) of 38 (rounded to the nearest ten-thousandth).

7)Construct a prediction interval estimate for SMI at a Temp of 38. What is the value of the lower bound of the interval (rounded to the nearest tenth)?

Answer 1

1)

x = mean annual temperature (Temp)

y = mortality rate (SMI) for a type of breast cancer in women

2)

Correlation coefficient (r) = 0.9 (=CORREL(Xi,Yi)

3)

H0​: ρ = 0

HA​: ρ not = 0

α = 0.05

rc ​= 0.602 (Use r table)

∣r∣ > rc ​= 0.602, Reject H0

There is sufficient evidence to support the claim of linear correlation because the absolute value of r is larger than the critical value from Table A-6 of 0.602.

4)

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.949879808
R Square	0.902271649
Adjusted R Square	0.891412944
Standard Error	4.892296138
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1988.770765	1988.770765	83.09200753	7.69148E-06
Residual	9	215.4110535	23.9345615
Total	10	2204.181818
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-55.62003454	15.0303308	-3.700519655	0.004916604	-89.62100502	-21.61906407	-89.62100502	-21.61906407
Temp	3.073402418	0.337162917	9.115481749	7.69148E-06	2.31068691	3.836117926	2.31068691	3.836117926

Y^ = -55.6 + 3.1*X

the slope of the regression line = 3.1

5)

the y-intercept of the regression line = -55.6

6)

If X = 38

Y^ = -55.6 + 3.1*X

Y^ = -55.6 + 3.1*38 = 62.2

7)

X0	38
Y^	62.2
X bar	44.3636
MSE	23.9345615
SSxx	210.55	SUM(X-X bar)^2
t c	2.262157163	Use t table
95% PI
LOWER	49.7	Y^-tc*SQRT(MSE*(1+1/n+(X0-Xbar)^2/SSxx))
UPPER	74.7	Y^+tc*SQRT(MSE*(1+1/n+(X0-Xbar)^2/SSxx))