Que 1: Which of the following is incorrect statement about datatypes employed in the
regression analysis.
(a) A typical time-series comprises observations about an entity across multiple
time-periods
(b) A typical cross-sectional data comprises observations of multiple entities from a
particular time
(c) Panel or longitudinal data comprises observations of multiple entities from
a particular time
(d) Panel or longitudinal data comprises observations of multiple entities from a
series of time-periods
Hint: Time-series observations include various attributes of an entity over multiple time-
periods. Cross-sectional data comprises multiple entity observations over a single
time-period. Panel or longitudinal data comprises multiple entity attributes being
observed over multiple time-periods.
Que 2: The following is an incorrect statement about the simple linear regression model
:Y= β0+β1X+u
(a) In this model X is considered to be exogenous and fixed
(b) In this model β0 is the intercept and also the unconditional mean of Y
(c) The conditional mean of Y , i.e., E(Y|X) is β0+β1X
(d) All the statements are correct.
Hint: Regression model considers X to be fixed from outside and thus exogenous. β0,
the intercept term is also the unconditional mean of Y, that is expected value of Y if X=0.
Conditional mean of Y, i.e., E(Y|X) is β0+β1X.
Que 3: The following is an incorrect statement in the context of regression and
correlation.
(a) Regression only measures the statistical strength of the relationship, not the
direction of causality. ``
(b) The direction of causality should come a priori from the theory.
(c) Correlation is a measure of linear association between the two variables, and
both the variables are treated in a symmetric manner
(d) All the statements are correct.
Hint: Regression provides the measure of statistical strength of the relationship. But the
direction of causality should come a priori from the theoretical underpinnings. In
contrast, correlation is only a measure of linear association between two variables.
Unlike regression, where there is a direction of causality, with correlation both the
variables are treated symmetrically.
Que 4: The following is an incorrect statement in the context of regression analysis
(a) Regression analysis aims to predict conditional mean values of a variable
(b) Regression analysis is based on minimizing the residual sum of squares.
(c) Regression analysis aims to predict conditional median values of a variable.
(d) All the statements are correct.
Hint: Regression analysis aims to predict the conditional mean values of the dependent
variable. This is obtained by minimizing the error sum of squares from the model.
Que 5-10: Using the information provided in the table below [X= Income, and Y= Weekly
Consumption Expenditure], answer the following questions.
X-> Income 80 100 120 140 160 180 200 220 240 260
55 65 79 80 102 110 120 135 137 150
60 70 84 93 107 115 136 137 145 152
65 74 90 95 110 120 140 140 155 175
Y Weekly
70 80 94 103 116 130 144 152 165 178
Cons Exp
75 85 98 108 118 135 145 157 175 180
88 113 125 140 160 189 185
115 162 191
Que 5: What is the unconditional mean of Y.
(a) 100-120
(b) 120-140
(c) 140-160
(d) 160-180
Hint: Unconditional mean is the average of all the observations: 7272/60=121.1
Que 6: What is the conditional mean of Y, given X=160, that is, E[Y|X=160].
(a) 100-120
(b) 120-140
(c) 140-160
(d) 160-180
Hint: Conditional mean of Y is the average of Y given X=160. E[Y|X=160]=678/6= 113
Que 7: What is the conditional mean of Y, given X=240, that is, E[Y|X=240].
(a) 100-120
(b) 120-140
(c) 140-160
(d) 160-180
Hint: Conditional mean of Y is the average of Y given X=240. E[Y|X=240]=966/6= 161
Que 8: What is the standard deviation of X, i.e., σx.
(a) 30-40
(b) 40-50
(c) 50-60
(d) 60-70
̅ )𝟐
Σ(𝑿𝒊 −𝑿
Hint: σx2= , σx=57.32
𝑛
Que 9: What is the Covariance between X and Y, i.e., σxY.
(a) 1600-1700
(b) 1700-1800
(c) 1800-1900
(d) 1900-2000
̅ )(𝒀𝒊 −𝒀
∑(𝑿𝒊 −𝑿 ̅)
Hint: σxy= , σxy=1971.93
𝑛
Que 10: If the following regression model is run, Y=β0+β1X+error. What is the value of β1
here.
(a) 0.00-0.25
(b) 0.25-0.50
(c) 0.50-0.75
(d) 0.75-1.00
Hint: β1= σxy/ σx2= 1971.93/(57.32)^2=0.60
