The height (in inches) and blood pressure (mm Hg) of 32 female athletes were use
ID: 3313548 • Letter: T
Question
The height (in inches) and blood pressure (mm Hg) of 32 female athletes were used to develop a model for the relationship between height and blood pressure in female athletes. A scatterplot was done to show that a linear model is appropriate. SPSS output is provided below.
1.028
a.How much would you expect blood pressure to increase for each 1-inch increase in height? Include the units. [2]
Final Answer: _______________________________
b.Give the equation of the least squares regression line for predicting blood pressure from height. [2]
Final Answer: _______________________________
[Bonus Question] Suppose Janie is 70 inches tall and has a blood pressure of 90 mm Hg. Based on the least squares regression line, what is the value of the residual for Janie? [Bonus 2]
Final Answer: ____________________
The unstandardized coefficient value of 0.25 given in the SPSS output is an example of:
[2] Circle all that are correct:
a sample statistic a population parameter a test statistic
a slope of the regression line for the population
an intercept of the regression line for the sample
f. The researcher would like to test if there is a significant linear relationship between height and blood pressure. Write out the appropriate hypotheses, the value of the test statistic, and the corresponding p-value. Then circle the appropriate conclusion using a 5% significance level.
[6]
H0: ___________________________
Ha: ___________________________
Test statistic value = ______________ p-value = ____________________
Therefore, it appears that (circle one):
There is a significant linear relationship between height and blood pressure in the population of female athletes represented by this sample.
There is no significant linear relationship between height and blood pressure in the population of female athletes represented by this sample.
g. What is the coefficient of determination? Interpret this value. [2]
h. Calculate the 95% confidence interval for the population slope. [2]
Final Answer: ________________________.
i. [Bonus question] Fill in the blank in the ANOVA SPSS output. [2 bonus points]
Final Answer: ________________________.
j. If you had to test whether the population slope in this context is negative which of the following test statistic would be the appropriate? Circle answer(s) [2]
t test statistic
F test statistic
?1 test statistic
Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.758 0.574 0.561.028
Explanation / Answer
Result:
a.How much would you expect blood pressure to increase for each 1-inch increase in height? Include the units. [2]
Final Answer: 0.38 mm Hg
b.Give the equation of the least squares regression line for predicting blood pressure from height. [2]
Final Answer: blood pressure = 0.25+0.38*height
[Bonus Question] Suppose Janie is 70 inches tall and has a blood pressure of 90 mm Hg. Based on the least squares regression line, what is the value of the residual for Janie? [Bonus 2]
Predicted blood pressure = 0.25+0.38*70 =26.85
Residual =90-26.85 = 63.15
Final Answer: 63.15
The unstandardized coefficient value of 0.25 given in the SPSS output is an example of:
[2] Circle all that are correct:
an intercept of the regression line for the sample
f. The researcher would like to test if there is a significant linear relationship between height and blood pressure. Write out the appropriate hypotheses, the value of the test statistic, and the corresponding p-value. Then circle the appropriate conclusion using a 5% significance level.
[6]
H0: =0
Ha: 0
Test statistic value = 6.36 p-value = 0.000001
Therefore, it appears that (circle one):
There is a significant linear relationship between height and blood pressure in the population of female athletes represented by this sample.
.
g. What is the coefficient of determination? Interpret this value. [2]
R square = 0.574
57.4% of variance in blood pressure is explained by height.
h. Calculate the 95% confidence interval for the population slope. [2]
lower limit = 0.38-2.042*0.06 =0.25748
upper limit = 0.38+2.042*0.06 =0.50252
Final Answer: (0.2575, 0.5025).
i. [Bonus question] Fill in the blank in the ANOVA SPSS output. [2 bonus points]
Final Answer: F=40.32
j. If you had to test whether the population slope in this context is negative which of the following test statistic would be the appropriate? Circle answer(s) [2]
t test statistic
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