Regression Analysis for Exam Score and Market Assessment

The provided assignment is a detailed solution to a regression analysis problem. It involves analyzing the relationship between exam scores and independent variables like homework hours and class hours, as well as conducting a market assessment by regressing log price against Friday. The solution includes coefficient values, correlation coefficients, and estimated response of consumer demand to changes in log price. It also discusses the importance of including additional variables in regression models, such as teacher teaching style and parents' influence on children's studies.

ECONOMETRICS

TABLE OF CONTENTS
QUESTION 1: RENTALASSESSMENT.......................................................................................1
a. Regressing Rental and IC.............................................................................................................1
b. Exhibit heteroscedasticity.......................................................................................................2
c. Normal distribution of Rental and INC...................................................................................3
d. Residuals in model are normally distributed...........................................................................4
e. Model misspecification...........................................................................................................6
QUESTION 2: RENTALASSESSMENT.......................................................................................7
a. Regressing logwage on logiq..................................................................................................7
b. Exhibit heteroscedasticity.......................................................................................................8
c. Normally distributed of LOGRENTAL and LOGINC...........................................................9
d. Normally distributed of residuals.........................................................................................10
e. Model specification...............................................................................................................11
QUESTION 3: EXAM SUCCESS................................................................................................11
a. Regressing exam score on class hours along with estimating and interpreting coefficient. .11
b. Testing hypothesis that exam score is not related to home hours.........................................12
c. Regressing exam score on class hours and home work.........................................................12
d. Amount of variation in Exam score across students by home work and class hours............13
e. Estimate of coefficient is different in (a) and (c)..................................................................13
f. Advice to students to attend class and home work................................................................13
g. Variables must be included in regression..............................................................................14
QUESTION 4: MARKET ASSESSMENT...................................................................................14
a. Regressing Log price and Friday...........................................................................................14
b. Predicted values purports for represent.................................................................................14
c. Estimate response of consumer demand to change in log price............................................14
d. Is equation identified.............................................................................................................15

QUESTION 1: RENTALASSESSMENT
a. Regressing Rental and IC
Null hypothesis: H0- There is no statistically significant relationship in Rental and IC.
Alternative hypothesis: H1- There is statistically significant relationship in Rental and IC.
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression 1409857.177 1 1409857.177 437.086 .000b
Residual 406423.698 126 3225.585
Total 1816280.875 127
a. Dependent Variable: rent
b. Predictors: (Constant), income
Interpretation: The table is replicating regression model which forecast that dependent
variables are significantly well. In the above scenario, p value is less than 0.05 then null
hypothesis is rejected and statistically proved that there is significant relationship in rental and
IC.
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b. Exhibit heteroscedasticity
Interpretation: The above graph is reflected to trace heteroscedasticity as scatter plot of
the residuals which appeared under Normal Probability plot. The data is heteroscadicitic because
data points scattered in the chart.
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c. Normal distribution of Rental and INC
There is bell shape curve in the chart and it is normally distributed.
.
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d. Residuals in model are normally distributed
The residuals abnormal distribution is interpreted with use of Q-Q plot, as distribution is
not normal because points are not clustered around horizontal line.
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There is absence of bell shape curve from the charts given above which are indicating that
data is not normally distributed.
e. Model misspecification
In the chart it can be seen that data points are closed to each other and moving upward from
left to right. Hence, it can be said that there is linear relationship between both. Breusch pagan
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test is the one of the test that is used to measure heteroskedasticity which test whether the
variance of errors from regression is dependent on the values of the independent variable. For
normality testing Shapiro Wilk test is used which help in determining whether there is normal
distribution in the data set considering significance level.
QUESTION 2: RENTALASSESSMENT
a. Regressing logwage on logiq
Null hypothesis: H0- There is no statistically significant relationship in LOGRENTAL and
LOGINC.
Alternative hypothesis: H1- There is statistically significant relationship in LOGRENTAL and
LOGINC.
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression 10.396 1 10.396 357.676 .000b
Residual 3.662 126 .029
Total 14.058 127
a. Dependent Variable: logrent
b. Predictors: (Constant), logincome
Interpretation: The above table is stating model of regression which directly predicts the
dependent variables are significantly well with context of significance value. According to
criteria of 0.05, here p value is less than this so alternative hypothesis is accepted. It could be
elaborated about presence of statistically significant relationship in LOGRENTAL and LOGINC.
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b. Exhibit heteroscedasticity
Interpretation: The above graph is showing scatter plot of LOGRENTAL and LOGINC
of its residuals. It has been observed that data is heteroscadicitic because of data points scattered
in the chart. If line has been stated throughout the data, it would look like a cone.
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c. Normally distributed of LOGRENTAL and LOGINC
Data is normally distributed as indicated by bell shape curve in the chart.
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d. Normally distributed of residuals
The residuals of model are normally distribution because they are in random pattern .
Hence, this fit for linear model.
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e. Model specification
In the chart it can be seen that data points are closed to each other and moving upward from left
to right. Model is accurate as reflected by the chart. Breusch pagan test is the one of the test that
is used to measure heteroskedasticity. In respect to normality test Shapiro Wilk test is employed.
QUESTION 3: EXAM SUCCESS
a. Regressing exam score on class hours along with estimating and interpreting coefficient
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
1
(Constant) 22.729 .842 26.993 .000
HOMEWO
RK .036 .009 .147 3.841 .000
a. Dependent Variable: EXAMSCORE
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Interpretation: The above table is reflecting coefficient value of dependent and independent
variable. It can be seen that coefficient value is 0.036 which is low but have p value 0.00<0.05
which is indicating that there is significant difference between both variables in terms of rate of
variation.
b. Testing hypothesis that exam score is not related to home hours
H0: There is no significant association between exam score and home hours.
H1: There is significant association between exam score and home hours.
Correlations
EXAMSCO
RE
HOMEWO
RK
EXAMSCO
RE
Pearson
Correlation 1 .147**
Sig. (2-tailed) .000
N 680 674
HOMEWOR
K
Pearson
Correlation .147** 1
Sig. (2-tailed) .000
N 674 674
**. Correlation is significant at the 0.01 level (2-tailed).
Interpretation
Correlation value is 0.147 which is low. However, value of level of significance is 0.00<0.05
which is indicating that there is significant association between both variables.
c. Regressing exam score on class hours and home work
Null hypothesis: H0- There is no statistically significant relationship in Exam score with Class
hours and home work.
Alternative hypothesis: H1- There is statistically significant relationship in Exam score with
Class hours and home work.
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 21.801 .973 22.415 .000
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CLASSHOU
RS .083 .044 .093 1.896 .058
HOMEWOR
K .022 .012 .089 1.814 .070
a. Dependent Variable: EXAMSCORE
Correlation coefficient of class work is 0.08 which is quite low and level of significance
is P = 0.05=0.05 which is indicating that due to change in class hours any big change does not
come in marks. On other hand, in case of homework coefficient value is 0.02 and level of
significance is 0.07.0.05 which is again indicating that change in homework hours does not bring
big change in exam score.
d. Amount of variation in Exam score across students by home work and class hours
Model Summary
Model R R Square Adjusted R
Square
Std. Error of
the Estimate
1 .163a .027 .024 4.668
a. Predictors: (Constant), HOMEWORK, CLASSHOURS
Value of R square is 0.027 which means that 2% deviation in independent variable is explained
by dependent variable. Hence, only 2% deviation in score is explained by variable homework
and class hours.
e. Estimate of coefficient is different in (a) and (c)
There is different coefficient value of the variable home hours to the dependent variable
exam score in two models. This happened because independent variables which are class hours
and office hours have very high correlation of 0.62. Hence, there is multi collinearity and due to
this reason coefficient value of variable home hours is different in case of both models.
f. Advice to students to attend class and home work
The students must attend class hours and do their home works as both are equally
correlated to their exam score as 0.148 and 0.147 respectively. However, correlation value is
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quite low which is indicating that apart from class and home work there are some other factors
that may have huge influence on student score.
g. Variables must be included in regression
Teacher teaching style and parents influence on children in respect to study as well as
parent’s attentiveness on student in respect to education are some of factors that can be taken in
to account in regression model.
QUESTION 4: MARKET ASSESSMENT
a. Regressing Log price and Friday
Null hypothesis: H0- There is no statistically significant relationship in Log price and Friday.
Alternative hypothesis: H1- There is statistically significant relationship in Log price and
Friday.
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression .102 1 .102 .615 .435b
Residual 15.599 94 .166
Total 15.701 95
a. Dependent Variable: logprice
b. Predictors: (Constant), friday
Value of level of significance is 0.435>0.05 which is indicating that there is no significant
impact of independent variable on dependent variable.
b. Predicted values purports for represent
In the above scenario, its significant value is greater than 0.05 as its null hypothesis is
accepted. It could be elaborated that there is no statistical significant relationship in Friday and
log price.
c. Estimate response of consumer demand to change in log price
ANOVAa
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Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression .618 1 .618 .615 .435b
Residual 94.382 94 1.004
Total 95.000 95
a. Dependent Variable: Standardized Predicted Value
b. Predictors: (Constant), logprice
Value of level of significance is 0.435>0.05 which is indicating that there is no significant
difference between predicted value and independent variable which log price.
d. Is equation identified
Equation = 0.049+0.198* - .492 logprice
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