Do the data BodyFat2.xlsx indicate linear association between Weight and %Body Fat? a Fit a model predicting the %Body F
Posted: Wed May 04, 2022 12:11 pm
Do the data BodyFat2.xlsx indicate
linear association
between Weight and %Body
Fat?
a Fit a model predicting the %Body Fat from the Weight.
Explanatory variable = [
Select ] ["%BodyFat", "Weigth"]
Response variable = [
Select ] ["%BodyFat",
"Weigth"]
Estimated [ Select ]
["%BodyFat", "Weight"] =
[ Select ]
["2.1950", "143.9324", "-30.8508",
"0.2715"] + [
Select ] ["-30.8508", "143.9324",
"2.1950", "0.2715"] ×
[ Select ] ["%BodyFat",
"Weight"]
b) Discuss the assumptions for inference.
Straight enough condition: The scatterplot is
[ Select ] ["not
straight enough to try a linear model.", "straight enough to try a
linear model."]
Independence assumption: The residuals plot
[ Select ]
["shows a trend", "is scattered"] .
Equal variance assumption: The spread of the residuals
is [ Select ]
["not consistent",
"consistent"] .
Nearly Normal condition, outlier condition: The boxplot of
the residuals is [ Select
] ["symmetric without any possible
outlier", "skewed with one possible outlier", "symmetric with one
possible outlier"] .
Since conditions have [
Select ] ["been satisfied", "not been
satisfied"] , the sampling distribution of the
regression slope can be modeled by a Student’s t-model
with [ Select ]
["20 degrees of freedom", "19 degrees of
freedom", "18 degrees of freedom"] . We will use
a [ Select ]
["regression slope t-test", "regression
intercept t-test"] .
c) Test an appropriate hypothesis using 2% level of significance
and state your
1. Hypotheses:
H0: [ Select
] ["b1 ≠ 0", "β1 = 0", "b1 = 0", "β1 ≠
0"] (There is [
Select ] ["no linear relationship", "a
linear relationship"] between weight and percent body
fat.)
HA: [ Select
] ["β1 = 0", "b1 ≠ 0", "β1 ≠ 0", "b1 =
0"] (There is
[ Select ] ["a linear relationship",
"no linear relationship"] between weight and percent
body fat.)
2. Test statistic:
t = [ Select ]
["-3.0752", "5.1519"]
P-value = [ Select ]
["6.69106E-05", "0.0065"]
R2 = [
Select ] ["0.7719", "0.5959"]
3. Decision rule:
4. Conclusion:
Based on the sample and at 2% level of significance, there
is [ Select ]
["strong evidence", "no evidence"] of
a linear relationship between weight and percent body fat. People
with more weight tend to have
[ Select ] ["lower",
"higher"] percentage of body fat.
c) Find a 98% confidence interval for the slope of the
regression line.
98% CI = ( [ Select ]
["3.2824", "0.1608", "1.1075", "0.4060",
"0.1370", "0.3822"] ,
[ Select ] ["1.1075", "0.3822",
"0.4060", "3.2824", "0.1608", "0.1370"] )
linear association
between Weight and %Body
Fat?
a Fit a model predicting the %Body Fat from the Weight.
Explanatory variable = [
Select ] ["%BodyFat", "Weigth"]
Response variable = [
Select ] ["%BodyFat",
"Weigth"]
Estimated [ Select ]
["%BodyFat", "Weight"] =
[ Select ]
["2.1950", "143.9324", "-30.8508",
"0.2715"] + [
Select ] ["-30.8508", "143.9324",
"2.1950", "0.2715"] ×
[ Select ] ["%BodyFat",
"Weight"]
b) Discuss the assumptions for inference.
Straight enough condition: The scatterplot is
[ Select ] ["not
straight enough to try a linear model.", "straight enough to try a
linear model."]
Independence assumption: The residuals plot
[ Select ]
["shows a trend", "is scattered"] .
Equal variance assumption: The spread of the residuals
is [ Select ]
["not consistent",
"consistent"] .
Nearly Normal condition, outlier condition: The boxplot of
the residuals is [ Select
] ["symmetric without any possible
outlier", "skewed with one possible outlier", "symmetric with one
possible outlier"] .
Since conditions have [
Select ] ["been satisfied", "not been
satisfied"] , the sampling distribution of the
regression slope can be modeled by a Student’s t-model
with [ Select ]
["20 degrees of freedom", "19 degrees of
freedom", "18 degrees of freedom"] . We will use
a [ Select ]
["regression slope t-test", "regression
intercept t-test"] .
c) Test an appropriate hypothesis using 2% level of significance
and state your
1. Hypotheses:
H0: [ Select
] ["b1 ≠ 0", "β1 = 0", "b1 = 0", "β1 ≠
0"] (There is [
Select ] ["no linear relationship", "a
linear relationship"] between weight and percent body
fat.)
HA: [ Select
] ["β1 = 0", "b1 ≠ 0", "β1 ≠ 0", "b1 =
0"] (There is
[ Select ] ["a linear relationship",
"no linear relationship"] between weight and percent
body fat.)
2. Test statistic:
t = [ Select ]
["-3.0752", "5.1519"]
P-value = [ Select ]
["6.69106E-05", "0.0065"]
R2 = [
Select ] ["0.7719", "0.5959"]
3. Decision rule:
4. Conclusion:
Based on the sample and at 2% level of significance, there
is [ Select ]
["strong evidence", "no evidence"] of
a linear relationship between weight and percent body fat. People
with more weight tend to have
[ Select ] ["lower",
"higher"] percentage of body fat.
c) Find a 98% confidence interval for the slope of the
regression line.
98% CI = ( [ Select ]
["3.2824", "0.1608", "1.1075", "0.4060",
"0.1370", "0.3822"] ,
[ Select ] ["1.1075", "0.3822",
"0.4060", "3.2824", "0.1608", "0.1370"] )