Question

The data file Demographics was used in a simple linear regression model where Unemployment Rate is the response variable and Cost of Living is the explanatory variable. You may refer to the previous two questions for the regression model if you wish. The anova function in R was used to obtain the breakdown of the sums of squares for the regression model. This is shown below: > anova(myreg)Analysis of Variance Table Response: Unemployment Df Sum Sq Mean Sq F value Pr(>F) Cost_of_living 1 32.44 32.439 7.9687 0.005515 ** Residuals 129 525.14 4.071 Based on the ANOVA table, what is R2 for the regression model?

Answer #1

**Solution:**

Given:

SSR = Sum of squares due to regression = 32.44

SSE = Sum of squares due to error ( Residual) = 525.14

Thus

SST = SSR + SSE

SST = 32.44 + 525.14

SST = 557.58

Source of variation | df | Sum of Squares | Mean Square | F-Statistic | Pr(>F) |
---|---|---|---|---|---|

Cost of Living | 1 | 32.44 | 32.439 | 7.96870 | 0.005515 |

Residual | 129 | 525.14 | 4.071 | ||

Total | 130 | 557.58 |

We have to find R2.

Response: Interval
Df Sum Sq Mean Sq F value Pr(>F)
Duration 1 39358 39358 1092 < 2.2e-16 ***
Residuals 268 9659 36
R2 is equal 0.8029409.
Question: Produce the ANOVA(Analysis of variance) table for the
SLR model and interpret the results of the F-test. What is the coe
cient of determination for this model and how should you interpret
this summary measure?

A least-squares simple linear regression model was fit
predicting duration (in minutes) of a dive from depth of the dive
(in meters) from a sample of 43 penguins' diving depths and
times.
Calculate the R-squared value for the regression by filling in the
ANOVA table.
SS
df
MS
F-statistic
Regression
Residual
1182.955
Total
537814.901
0.91
0.0902
0.0022
4.92461123041641e-23

Use the information and general form of the ANOVA table for
multiple regression from class or from page 613 of the book to
complete the table, find the F-statistic, and find R2.
Source
DF
SS
MS
F
Model
4
70
Error
Total
33
524
For question 17, what percentage of the variation in the
response variable is explained by the explanatory variables?
(report as %)
What is the range for the p-value for question 17?
>0.100
0.050 to 0.100
0.025...

22. We fit a simple linear regression model using price (in
dollars) to predict the number of packets of dog biscuits sold per
day. The regression equation is y = 98.1 - 9.8x, and R2 =
0.5275.
Explain how to interpret the R2 in the context of this problem.:
*
(A) 52.75% of the variation in the price is explained by the number
of packets of dog biscuits sold per day.
(B) 52.75% of the variation in the number of...

The statistical model
for simple linear regression is written as μy
= β0 +
β1*x, where μy
represents the mean of a Normally distributed response variable and
x represents the explanatory variable. The parameters
β0 and β1 are estimated,
giving the linear regression model defined by
μy = 70 + 10*x , with standard
deviation σ = 5.
(multiple choice
question)
What is the
distribution of the test statistic used to test the null hypothesis
H0 : β1 =
0...

8.) Now, do a simple linear regression model for LifeExpect2017
vs. AverageDailyPM2.5. For credit, provide the summary
output for this simple linear regression model.
> Model2 <- lm(LifeExpect2017~ AverageDailyPM2.5)
> summary(Model2)
Call:
lm(formula = LifeExpect2017 ~ AverageDailyPM2.5)
Residuals:
Min 1Q Median 3Q Max
-17.1094 -1.7516 0.0592 1.7208 18.4604
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 81.6278 0.2479 329.23 <2e-16 ***
AverageDailyPM2.5 -0.4615 0.0267 -17.29 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘...

Consider the simple linear regression model y=10+30x+e where the
random error term is normally and independently distributed with
mean zero and standard deviation 1. Do NOT use
software. Generate a sample of eight observations, one each at the
levels x= 10, 12, 14, 16, 18, 20, 22, and 24.
Do NOT use software!
(a) Fit the linear regression model by least squares and find
the estimates of the slope and intercept.
(b) Find the estimate of ?^2 .
(c) Find...

4. Data on the unemployment rate and alcohol sales were
analyzed. The following regression equation was computed from a
sample of 18 data points.
?̂ = 3 . 5 9 + . 7 2 ?
(A) Complete this ANOVA table. (9)
Source
SS
df
MS
F
Regression
Error
301.1
Total
403.8
(B) Determine the standard error of estimate. (Round to 3
decimals.) (9)
(C) Determine the coefficient of determination. (Round to 3
decimals.) (9)
(D) Determine the correction coefficient. Clearly...

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.816
.666
.629
1.23721
a. Predictors:
(Constant),x
ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig
Regression
Residual
Total
27.500
13.776
41.276
1
9
10
27.500
1.531
17.966
.002b
a. Dependent Variable: Y
b. Predictors: (Constant), X
Coefficients
Model
Understand Coefficients
B
Std Error
Standardized
Coefficients
Beta
t
Sig
1 (Constant)
x
3.001
1.125
.500
.118
.816
2.667...

Assume you ran a multiple regression to gain a better
understanding of the relationship between lumber sales, housing
starts, and commercial construction. The regression uses lumber
sales (in $100,000s) as the response variable with housing starts
(in 1,000s) and commercial construction (in 1,000s) as the
explanatory variables. The estimated model is Lumber Sales =
β0 +β1Housing Starts +
β2 Commercial Constructions + ε. The
following ANOVA table summarizes a portion of the regression
results.
df
SS
MS
F
Regression
2...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 8 minutes ago

asked 17 minutes ago

asked 28 minutes ago

asked 33 minutes ago

asked 35 minutes ago

asked 40 minutes ago

asked 47 minutes ago

asked 55 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago