12.4 Study the following Minitab output from a regression analysis
to predict y from x.
a. What is the equation of the regression
model?
b. What is the meaning of the coefficient of
x?
c. What is the result of the test of the slope of
the regression model? Let α = .10.Why is the t ratio
negative?
d. Comment on r^{2} and the
standard error of the estimate.
e. Comment on the relationship of the F
value to the t ratio for x.
f. The correlation coefficient for these two
variables is  0.7918. Is this result surprising to you? Why or why
not?
Regression Analysis: Y versus X
The regression equation is
Y = 67.2  0.0565 X
Predictor 
Coef 
SE Coef 
T 
P 


Constant 
67.231  5.046  13.32  0.000  
X 
0.05650  0.01027  5.50  0.000  
S = 10.32  RSq = 62.7% 
RSq(adj) = 
60.6%  
Analysis of Variance 

Source 
DF 
SS 
MS 
F 
P 
Regression 
1  3,222.9  3,222.9  30.25  0.000 
Residual Error 
18  1,918.0  106.6  
Total 
19  5,141.0 
*(Round your answer to 1 decimal
places.)
**(Round your answer to 4 decimal
places.)
***(Round your answer to 2 decimal
places.)
a. The regression equation is: ŷ = enter
a number rounded to 1 decimal place * 
enter a number rounded to 4 decimal places
** x
b. For every unit of increase in the value of
x, the predicted value of y will select an
option
decreaseincrease by enter a number rounded to 4
decimal places **.
c. The t ratio for the slope is enter a
number rounded to 2 decimal places ***
with an associated pvalue of .000.
d. r^{2} is enter a number
rounded to 1 decimal place *% of the
variability of y is accounted for by x. This is
select an option
lowonly a modesthigh proportion of predictability. The
standard error of the estimate is enter a number rounded to 2
decimal places ***. This is select an
option
bestnot good interpreted in light of the data and the
magnitude of the data.
e. The F value which tests the overall
predictability of the model is enter a number rounded to 2 decimal
places ***. For simple regression
analysis, this equals the value of select an option
square of tsquare of Ssquare of r.
f. The select an option
negativepositive is not a
surprise because the slope of the regression line is also select an
option
negativepositive indicating an select an
option
inversedirect relationship between x and
y.
Get Answers For Free
Most questions answered within 1 hours.