Question

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks.

Completion Percentage | 56 | 57 | 64 | 65 | 66 |
---|---|---|---|---|---|

Interception Percentage | 4.5 | 3 | 2.5 | 2 | 1.5 |

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y^ is given by?

Step 4 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6: Find the estimated value of y when x=65. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer #1

Step 1: Sum of *X* = 308

Sum of *Y* = 13.5

Mean *X* = 61.6

Mean *Y* = 2.7

Sum of squares (*SS _{X}*) = 89.2

Sum of products (

Regression Equation = ŷ =

Step 2: *a* = M_{Y} - *b*M_{X} =
2.7 - (-0.22*61.6) = 16.235

Step 3: This value is same as slope so answer is -0.220

Step 4:

So answer is False

Step 5: Regression equation is

ŷ = -0.220*X* + 16.235

For x=65, y=-0.220**65* + 16.235=1.935

Step 6. *X Values*

∑ = 308

Mean = 61.6

∑(X - M_{x})^{2} = SS_{x} = 89.2

*Y Values*

∑ = 13.5

Mean = 2.7

∑(Y - M_{y})^{2} = SS_{y} = 5.3

*X and Y Combined*

*N* = 5

∑(X - M_{x})(Y - M_{y}) = -19.6

*R Calculation*

r = ∑((X - M_{y})(Y - M_{x})) /
√((SS_{x})(SS_{y}))

r = -19.6 / √((89.2)(5.3)) = -0.901

So coefficient of determination is r^2=0.812

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks. Completion
Percentage 57 59 61 65 65 Interception Percentage 4.8 4.7 4.5 3.1
1.1 Table
Step 2 of 5 : Calculate the estimated variance of errors, s2e.
Round your answer to three decimal places.
b1=−0.3727
b0=26.5238
SSE=2.842

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks. Completion
Percentage 57 59 61 65 65 Interception Percentage 4.8 4.7 4.5 3.1
1.1 Table
Step 3 of 5 : Calculate the estimated variance of slope, s2b1.
Round your answer to three decimal places.
b1=−0.3727
b0=26.5238
SSE=2.842
s2e=0.947

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks. Completion
Percentage 57 59 61 65 65 Interception Percentage 4.8 4.7 4.5 3.1
1.1 Table
Step 5 of 5 : Construct the 80% confidence interval for the
slope. Round your answers to three decimal places.

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks. Completion
Percentage 61 61 62 65 65 Interception Percentage 4.3 2.9 1.6 1.2
1.2 Table Step 1 of 5 : Calculate the sum of squared errors (SSE).
Use the values b0=35.7312 and b1=−0.5333 for the calculations.
Round your answer to three decimal places.

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks. Completion
Percentage 57 59 61 65 65 Interception Percentage 4.8 4.7 4.5 3.1
1.1 Table
Step 1 of 5 : Calculate the sum of squared errors (SSE). Use the
values b0=26.5238 and b1=−0.3727 for the calculations. Round your
answer to three decimal places.

The following table compares the completion percentage and
interception percentage of 55 NFL quarterbacks.
Completion Percentage
63
64
64
65
66
Interception Percentage
3.3
2.9
2.8
2
1.7
Step 5 of 5 :
Construct the 80% confidence interval for the slope. Round your
answers to three decimal places.

The following table compares the completion percentage and
interception percentage of 55 NFL quarterbacks.
Completion Percentage Interception Percentage
55 4
61 4
63 3.9
63 3
65 1.1
Step 1 of 5: Calculate the sum of squared errors (SSE). Use the
values b0=15.8545b0=15.8545 and b1=−0.2061b1=−0.2061 for the
calculations. Round your answer to three decimal places
Step 2 of 5: Calculate the estimated variance of errors, s2ese2.
Round your answer to three decimal places
Step 3 of 5: Calculate the estimated...

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks.
Completion Percentage
55
57
59
61
62
Interception Percentage
4.1
3.9
3.2
2.8
1.9
Step 1 of 5: Calculate the sum of squared errors (SSE). Use the
values b0=20.6024 and b1=−0.2963 for the calculations. Round your
answer to three decimal places.
Step 2 of 5: Calculate the estimated variance of errors, Round
your answer to three decimal places.
Step 3 of 5: Calculate the estimated variance...

The following table compares the completion percentage and
interception percentage of 5 NFL quarterbacks.
Completion Percentage
55
58
58
60
64
Interception Percentage
4.7
4.3
3.8
3.7
2.8
Step 5 of 5 : Construct the 95% confidence interval
for the slope. Round your answers to three decimal places.
.
Previous Answers
b1 = - 0.2091
b0 = 16.1969
SSE = 0.128
s2e = 0.043
s2b1 = 0.001

The following table compares the completion percentage and
interception percentage of 55 NFL quarterbacks.
Completion Percentage
55
58
58
60
64
Interception Percentage
4.7
4.3
3.8
3.7
2.8
Step 4 of 5 :
Construct the 90% confidence interval for the slope. Round your
answers to three decimal places.
Lower endpoint: ____________
Upper endpoint: ____________
.
Previous Answers:
b1 = -0.2091
b0 = 16.1969
SSE = 0.128
s^2e = 0.043
s^2b1 = 0.001

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