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000 /af/servlet/quiz?quiz action-takeQuiz&quiz; probGuid-ONAPCOA801010000003e822db00900008ct-kelly.huls Ao Aa 6. EOC Practice problem Some types of algae have the potential to cause damage to river ecosystems. The accompanying data on algae colony density (7) and rock surface area (x) for nine rivers is based on data that appeared in a scatterplot in a paper In the journal Aquatic Ecology (2010: 33-40). X 50 54 49 78 45 35 69 46 50 Y 153 48 23 36 38 182 14 185 26 Note: In the following questions, the exact values in your answers may differ from those provided due to rounding differences. Select the responses that are closest to your answers. Compute the equation of the least squares regression line. O y = 78.33 +52.89x y =-3.14x O y -3.14 +244.411x O y 244.41 3.14x What is the value of r2 for this data set? r2 =-0.57 r2 = 244.41 r2 = 0.57 O r2 = 0.32 What is the value of se for this data set? se = 63.94 O se= 0.32 O se = 0.57 O se 56.39Explanation / Answer
Answer:
Regression line y=244.41-3.14x
r2 = 0.32
se=63.94
Relationship is negative ( coefficient is negative)
Relationship is moderate ( r=-0.564)
Regression Analysis
r²
0.319
n
9
r
-0.564
k
1
Std. Error
63.924
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
13,374.1065
1
13,374.1065
3.27
.1134
Residual
28,603.8935
7
4,086.2705
Total
41,978.0000
8
Regression output
confidence interval
variables
coefficients
std. error
t (df=7)
p-value
95% lower
95% upper
Intercept
244.6232
94.3547
2.593
.0358
21.5098
467.7366
x
-3.1441
1.7379
-1.809
.1134
-7.2537
0.9654
Regression Analysis
r²
0.319
n
9
r
-0.564
k
1
Std. Error
63.924
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
13,374.1065
1
13,374.1065
3.27
.1134
Residual
28,603.8935
7
4,086.2705
Total
41,978.0000
8
Regression output
confidence interval
variables
coefficients
std. error
t (df=7)
p-value
95% lower
95% upper
Intercept
244.6232
94.3547
2.593
.0358
21.5098
467.7366
x
-3.1441
1.7379
-1.809
.1134
-7.2537
0.9654
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