Question

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 r2 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 0.9482. Is this result surprising to you? Why or why not? Regression Analysis: Y versus X The regression equation is Y = 1.5698 + 0.04070 X Predictor Coef SE Coef T P Constant 1.5698 0.3381 4.64 0.001 X 0.04070 0.004312 9.44 0.000 S = 0.17 R-Sq = 89.9% R-Sq(adj) = 88.9% Analysis of Variance Source DF SS MS F P Regression 1 2.7980 2.7980 89.09 0.000 Residual Error 10 0.3141 0.0314 Total 11 3.1121 *(Round your answer to 1 decimal place.) **(Round your answer to 4 decimal places.) ***(Round your answer to 2 decimal places.)

a. The regression equation is: y Overscript ̂ EndScripts = ** + ** x

b. For every unit of increase in the value of x, the predicted value of y will by **.

c. The t ratio for the slope is *** with an associated p-value of .000.

d. r2 is *% of the variability of y is accounted for by x. This is proportion of predictability. The standard error of the estimate is ***. This is 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 ***. For simple regression analysis, this equals the value of .

f. The is not a surprise because the slope of the regression line is also indicating an relationship between x and y. Question Attempts: 0 of 2 used SAVE FOR LATER SUBMIT ANSWER

Answer #1

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 r2 and the
standard error of the estimate.
e. Comment on the relationship of the F
value to the...

From the following MINITAB regression analysis, what can you
conclude for the hypothesis test of Ho: β1=0 versus Ha: β1≠ 0 using
α=0.10?
The regression equation is
Test2 = 27.8 + 0.583 Test1
Predictor Coef SE Coef T P
Constant 27.82 25.00 1.11 0.278
Test1 0.5825 0.3070 1.90 0.071
S = 22.9977 R-Sq = 14.1% R-Sq(adj) = 10.2%
The null hypothesis would not be rejected and the conclusion
would be that the x variable is of no use...

Use the multiple regression output shown to answer the following
questions.
The regression equation is
Y=9.40+0.332X1+0.067X2-0.251X3
Predictor
Coef
SE Coef
T
P
Constant
9.395
6.858
1.37
0.184
X1
0.3316
0.8962
0.37
0.716
X2
0.0666
-0.0520
-1.28
0.214
X3
-0.2508
-0.1036
2.42
0.025
S=4.84768
R-Sq=15.0%
R-Sq(adj)=2.8%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
3
86.8
28.93
1.23
0.322
Residual Error
21
493.5
23.5
Total
24
580.3
a) Which variable might we try eliminating first to possibly
improve this...

Examine the Minitab output shown here for a multiple regression
analysis. How many predictors were there in this model? Comment on
the overall significance of the regression model. Discuss the
t ratios of the variables and their significance.
The regression equation is
y = 4.091 - 5.111x1+
2.662x2 + 1.557x3 +
1.141x4 +1.655x5 -
1.248x6 + 0.436x7 +
0.959x8 + 1.289x9
Predictor
Coef
Stdev
T
p
Constant
4.096
1.2884
3.24
.006
x1
-5.111
1.8700
2.73
.011
x2
2.662
2.0796
1.28...

Regression Analysis with a Minitab output
Assume that your company owns multiple retail outlets in cities
across the United States. You conduct a study to determine if daily
sales levels (in hundreds of dollars) can be predicted by the
number of competitors that are located within a one-mile radius of
each location and city population (in thousands of people).
Therefore, the dependent variable is SALES and the two independent
variables are NUMBER OF COMPETITORS and CITY POPULATION. Your
research team...

It has been speculated that there is a linear
relationship between Oxygen and Hydrocarbon Levels. Specifically,
Oxygen purity is assumed to be dependent on Hydrocarbon levels. A
linear regression is performed on the data in Minitab, and you get
the following results:
Regression Analysis: Purity-y versus Hydrocarbon
level-X
Predictor
Coef SE Coef
T P
Constant
74.283 1.593 46.62 0.000
Hydrocarbon level-X 14.947 1.317 11.35
0.000
S = 1.08653 R-Sq = 87.7% R-Sq(adj) =
87.1%
Analysis of Variance
Source
DF SS ...

The following output was obtained from a regression analysis of
the dependent variable Rating and an independent variable Price.
(10 points)
ANOVA
df
SS
MS
F
Regression
1
372.707
372.707
42.927
Residual
15
130.234
8.682
Total
16
502.941
Coefficients
Standard Error
t Stat
P-value
Intercept
45.623
3.630
12.569
0.000
Price
0.107
0.016
6.552
0.000
Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level of...

The following is a partial computer output of a
multiple regression analysis of a data set containing 20 sets of
observations on the dependent variable
The regression equation is
SALEPRIC = 1470 + 0.814 LANDVAL = 0.820 IMPROVAL + 13.5
AREA
Predictor
Coef
SE Coef
T
P
Constant
1470
5746
0.26
0.801
LANDVAL
0.8145
0.5122
1.59
0.131
IMPROVAL
0.8204
0.2112
3.88
0.0001
AREA
13.529
6.586
2.05
0.057
S = 79190.48
R-Sq = 89.7%
R-Sq(adj) = 87.8%
Analysis of Variance
Source...

1. The following output was obtained from a regression
analysis of the dependent variable Rating and an independent
variable
Price.
Anova
df SS MS f
Regression 1 301.701 301.701 32.94
Residual 15 128.221 9.1586
Total 16 429.922
Coefficients Standard Error T Stat P value
Intercept 45.623 3.630 12.569 0.000
Price .107 0.016 6.552 0.002
a. Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level...

Shown below is a portion of an Excel output for regression
analysis relating Y (dependent variable) and X (independent
variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is the estimated regression equation
that relates Y to X?
2. Is the regression relationship significant?
Use the p-value approach and alpha = 0.05 to answer this
question.
3. What is the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 19 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago