a) Interpret the coefficient on pfmeals in Model 2 (mathematically and statistically). b) is the coefficient on pfmeals in Model 1 biased compared to the coefficient on pfmeals in Model 2. If so, by how much? c) What 2 conditions would need to be true for bias of pfmeals to exist? Use only the information from Models 1 and 2 above to answer this question.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
a) Interpret the coefficient on pfmeals in Model 2 (mathematically and statistically).
b) is the coefficient on pfmeals in Model 1 biased compared to the coefficient on pfmeals in Model 2. If so, by how much?
c) What 2 conditions would need to be true for bias of pfmeals to exist? Use only the information from Models 1 and 2 above to answer this question.
![4. Here I use the test score data again. Let's say I ran two models to try to explain the
relationship between test scores and the percent of children in a school that receive free
meals (pfmeals).
Model 1 is a simple regression of test scores on pfmeals.
Model 2 is a multiple regression of test scores on pfmeals and pcol (percent of parents in
a particular school with a college degree).
Stata results are below.
Model 1:
• reg tscore pfmeals
Source
df
MS
Number of obs
4,889
F(1, 4887)
12921.42
Model
288035.863
288035.863
Prob > F
0.0000
Residual
4,887
22.2913505
R-squared
Adj R-squared
0.7255
Total
396973.693
4,888
81.2139307
Root MSE
4.7214
tscore
Coef.
Std. Err.
P>It|
[95% Conf. Interval]
pfmeals
-.2478825
.0021807
-113.67
0.000
-.2521576
-.2436074
cons
89.02932
.1373457
648.21
0.000
88.76006
89.29858](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafb5a5a0-4a07-47cd-9093-62e478b79856%2Fdb1441c9-53be-4c8f-9899-fd6862bdfb92%2Fw48e9d_processed.jpeg&w=3840&q=75)
![Model 2:
reg tscore pfmeals pcol
Source
df
MS
Number of obs
4,889
F (2, 4886)
8201.44
Model
305864.491
2 152932.246
Prob > F
0.0000
R-squared
Adj R-squared
Residual
91109.202
4,886 18. 6469918
0.7705
0.7704
Total
396973.693
4,888
81.2139307
Root MSE
4.3182
tscore
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
pfmeals
pcol
-.1517704
.0036932
-41.09
0.000
-.1590107
-.1445301
.1515683
.0049018
30.92
0.000
.1419586
.161178
_cons
79.41244
.3354241
236.75
0.000
78.75486
80.07003
I| || || I|||](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafb5a5a0-4a07-47cd-9093-62e478b79856%2Fdb1441c9-53be-4c8f-9899-fd6862bdfb92%2F2xa617f_processed.jpeg&w=3840&q=75)
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