Sta404 Regression and Correlation Analysis Practice/Sample Questions Lecture 6 to 10

STA404 Regression and Correlation Analysis
Practice/Sample Questions
Lecture 6 to 10

• 
  Solve these questions yourself without any help.
  
• 
  After your attempt, compare them yourself with lectures notes.
  
• 
  MCQs answers are given at the end.
  

MCQs (See answer at the end)

1. 
   How many dependent variable(s) may appear in a multiple regression?
   

1. 
   0
   
2. 
   1
   
3. 
   2
   
4. 
   3
   

2. 
   The multiple correlation coefficient R:
   

1. 
   Can vary within the range from -1 to +1, inclusive
   
2. 
   Can be less than the 0
   
3. 
   Can vary within the range from 0 to +1, inclusive
   
4. 
   Cannot achieve an absolute value of unity
   

3. 
   What value of level of significance is most frequently used in hypothesis testing?
   

1. 
   1%
   
2. 
   5%
   
3. 
   10%
   
4. 
   20%
   

4. 
   What is the value of y-intercept in the regression line ?
   

1. 
   -3X
   
2. 
   -3
   
3. 
   2
   
4. 
   -2
   

5. 
   In hypothesis testing simple correlation coefficient, if sample size is 15 then what is value of degree of freedom?
   

1. 
   13
   
2. 
   14
   
3. 
   15
   
4. 
   16
   

Descriptive Questions (2, 3 or 5 marks)

• 
  Write down the equation of regression model with one dependent and three independent variables.
  

• 
  In a study to determine a person’s yearly income 10 years after high school, it was found that the two biggest predictors are number of math courses taken and number of hours worked per week during a person’s senior year of high school. The multiple regression equation generated from a sample of 20 individuals is:
  

Let represent the number of mathematics courses taken and represent hours worked.
Explain what 4540 in the equation tell us.

• 
  Following are two normal equations obtained in a regression model.
  

Solve the both equation simultaneously so that you only left with equations that are free from “a”.

• 
  In a multiple regression equation notation b_12.3 what is meaning of subscript 1?
  

• 
  Explain the meaning of the notation of partial correlation coefficient r_23.1
  

• 
  For multiple regression model the simple correlation coefficients are r₁₂ = 0.492, r₁₃ = 0.927, r₂₃ = 0.758 Find the partial correlation coefficient r_31.2
  

• 
  If null hypothesis is Ho : β ≤ β0 then what will be the appropriate alternative hypothesis?
  

• 
  Write down the t-test formula that is used in the hypothesis testing of regression coefficient β.
  

• 
  By using the following data and regression line, calculate the value of .
  

• 
  Suppose you want to test the claim that null hypothesis Ho : α ≤ 0.5. After calculation, you obtained the calculated value of t-test as 2.82 and table (critical) value as 1.86. What will you conclude about the given claim?
  

• 
  Write down the names of steps that are used in hypothesis testing.
  

• 
  A random sample of 19 pairs of observations gives a coefficient of correlation of 0.65. Test the hypothesis, at 5% level of significance, that the correlation coefficient in the population is zero. (Write complete steps, computation and conclusion. Use t-test)
  

• 
  A sample of size 12 yielded r=0.32. Test H_o : ρ = 0 . Let α = 0.01
  

(Write complete steps, computation and conclusion. Use t-test)
= = = = = = = = =
Answers for MCQs:
1 (b)
2 (c)
3 (b)
4 (d)
5 (a)