Question

A low ?p-value for an independent variable (say, 0.04) indicates that the parameter estimate is not statistically significant; the variable should be discarded from future regression models.

Answer #1

**at 4% p-value is statistically significant**

**no variable should not be discarded from the future
value,**

P-value is defined as the lowest significance level at which a null hypothesis can be rejected. it is also known as the observed or exact level of significance. or exact probability of commuting type 1 error, for example, if the p-value is considered as 5% this means 5% of time value will be wrong.

we should not discard the variable because the variable is statistically significant, we use the rule that if the variable is not significant then we discard

**For any query please comment and please
upvote**

A small P-value indicates which of the following?
I) the parameter value indicated by the null hypothesis is not
plausible
II) the null hypothesis should be rejected in favor of the
alternative hypothesis
III) the difference between the parameter value and the value
specified in the null hypothesis is practically significant

A large studentized residual value indicates an outlier with
respect to:
Dependent variable only
Independent variables only
Both dependent and independent variables
Normality

Which one of the below is false?
Group of answer choices
In regression models, if p-value for a predictor is greater than
alpha, then that predictor is helpful to predict the response
variable.
High correlation correficents indicate strong relationship
between the variables of a regression model.
In regression models, we use p-values and alpha to determine if
the model is significant
Higher coefficient of determination values are desired in
regression models.

Multiple linear regression results:
Dependent Variable: Cost
Independent Variable(s): Summated Rating
Cost = -43.111788 + 1.468875 Summated Rating
Parameter estimates:
Parameter
Estimate
Std. Err.
Alternative
DF
T-Stat
P-value
Intercept
-43.111788
10.56402
≠ 0
98
-4.0810021
<0.0001
Summated Rating
1.468875
0.17012937
≠ 0
98
8.633871
<0.0001
Analysis of variance table for multiple regression model:
Source
DF
SS
MS
F-stat
P-value
Model
1
8126.7714
8126.7714
74.543729
<0.0001
Error
98
10683.979
109.02019
Total
99
18810.75
Summary of fit:
Root MSE: 10.441273
R-squared: 0.432...

A sample of 12 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=77, SST=88, summation (x_i-xbar)2=23,
summation (x_i-xbar)(y_i-ybar)=44.
Calculate the t test statistics to determine whether a
statistically linear relationship exists between x and y.
A sample of 7 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=24, SST=42
Using a 0.05 level of significance,...

QUESTION 4
Determine if each of the following statements is True or False
with full justification explaining your reasoning.
In multiple regression, a large R square indicates all
independent variables will have a significant effect on the
dependent variable if the significance level is set to 5%.
(1 mark)
In multiple regression, if an you have an independent variable
with a large p-value (close to 1), this independent variable cannot
be used to predict the dependent variable.
(1...

Parameter Estimates
Parameter
DF
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
1
-31.166890
2.880284
-10.82
<.0001
HouseholdInc
1
0.000097845
0.000027084
3.61
0.0003
DailyPM25
1
2.869205
0.147155
19.50
<.0001
PctSmokers
1
0.671836
0.048104
13.97
<.0001
PctObese
1
0.616837
0.080844
7.63
<.0001
PM25days
1
-0.244056
0.063909
-3.82
0.0001
OzoneDays
1
0.157997
0.035823
4.41
<.0001
PctDiabetic
1
1.164233
0.182226
6.39
<.0001
Regardless of the biological basis of disease or hypotheses,
statistically speaking, are any of your variables in your final
model...

What is the difference between
"statistically different from
0" and "significantly
different from 0"? say if my p-value for some co-efficient came out
to be 0.701 then how do we answer in terms of the two above? is it
like saying "since p>.10 the variable is not
statistically / significantly
different from 0" ? or which word (statistically vs
significantly) should I use ?

Suppose you conduct the modified White’s Test. You estimate the
regression with the squared residuals as the dependent variable and
predicted values and predicted values squared as independent
variables. From the regression results, you get the F-statistic is
0.353 with a p-value of 0.414. At a Level of Significance of 5%,
what does the modified White’s Test say about the Linear
Regression?
Group of answer choices
Heteroskedasticity is unlikely to be a problem with the Linear
Regression
Heteroskedasticity is likely...

A researcher would like to predict the dependent variable Y from
the two independent variables X1 and X2 for a sample of N=12
subjects. Using multiple linear regression, it has been confirmed
that the overall regression model is statistically significant at
α=0.05 with F(2,9)=5.66 (p=0.026). Calculate the 95% confidence
intervals for both partial slopes.
X1
X2
Y
66.2
60.5
75.2
41.6
19.3
26.9
52.5
57.2
50.4
60.9
42.5
44
75.2
49.3
71.6
63.9
57
56.5
36.8
62
45.6
38.5
61.4...

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