Using the following data with x as the independent variable and y as the dependent variable, answer the items.
x | -14 | -22 | 18 | 8 | 24 |
y | 64 | 253 | 159 | 9 | 347 |
Ans : Given data with x as the independent variable and y as the dependent variable
x | y |
-14 | 64 |
-22 | 253 |
18 | 159 |
8 | 9 |
24 | 347 |
Scatter plot of x versus y
b) to Compute correlation coefficient between x and y
To find correlation coefficient between x and y using following formula
x | y | (X-Mx)*(y-My) | (x-Mx)^2 | (y-My)^2 |
-14 | 64 | 1720.32 | 282.24 | 10485.76 |
-22 | 253 | -2147.68 | 615.04 | 7499.56 |
18 | 159 | -112.48 | 231.04 | 54.76 |
8 | 9 | -818.48 | 27.04 | 24774.76 |
24 | 347 | 3828.72 | 449.44 | 32616.36 |
14 | 832 | 2470.4 | 1604.8 | 75431.2 |
Mx = 2.8 , My =166.4
r= 0..224534
correlation coefficient between x and y is 0.2245
correlation coefficient 0.2245
Ans C):
Transform the x variable by squaring each value
x | x^2 | y |
-14 | 196 | 64 |
-22 | 484 | 253 |
18 | 324 | 159 |
8 | 64 | 9 |
24 | 576 | 347 |
Scatter plot of x^2 versus y
e) Ans :
To find correlation coefficient between x^2 and y using following formula
x | y | (X-Mx)*(y-My) | (x-Mx)^2 | (y-My)^2 |
-14 | 64 | 1720.32 | 282.24 | 10485.76 |
-22 | 253 | -2147.68 | 615.04 | 7499.56 |
18 | 159 | -112.48 | 231.04 | 54.76 |
8 | 9 | -818.48 | 27.04 | 24774.76 |
24 | 347 | 3828.72 | 449.44 | 32616.36 |
14 | 832 | 2470.4 | 1604.8 | 75431.2 |
r = 0.992756
correlation coefficient between x^2 and y is 0.9928
f)
Compare the correlation coefficient between x and y and X^2 and y
relationship between x and y is 0.2245
Relationship between x^2 and y is 0.9928
the Relationship between x^2 and y this is positive Relationship between X^2 and y
Using the following data with x as the independent variable and y as the dependent variable,...
The following information
regarding a dependent variable (Y in $1000) and an independent
variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
The following information regarding a dependent variable (Y in
$1000) and an independent variable (X) is provided.
Y
Dependent Variable
15
17
23
17
I. The least-squares estimate of the slope
equals:
II. The least-squares estimate of the intercept
equals:
III. If the independent variable increases by 2
units, the dependent variable is expected to
a. decrease by $300
b. decrease by $3000
c. decrease by $3
d. decrease by $2
e. none of the above
The letter corresponding...
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