The table shows the number of years of education of parent and the number of years...
The table shows the number of years of education of parent and the number of years of education of their child.
|
Years of Education of Parent |
13 |
9 |
7 |
12 |
12 |
10 |
11 |
|
Years of Education of their Child |
13 |
11 |
7 |
16 |
17 |
9 |
17 |
Determine the correlation coefficient and briefly describe the
relationship between the two variables.
Conduct a hypothesis test to determine if there is a significant
linear correlation between the two variables. What is the critical
value?
Conduct a hypothesis test to determine if there is a significant
linear correlation between the two variables. What is the test
statistic?
Conduct a hypothesis test to determine if there is a significant
linear correlation between the two variables. What is the
p-value?
If there is a significant linear correlation between the variables,
determine the regression equation
Homework Answers
Correlation Coefficient Calculation
r = 0.7729
Critical value
The sample size is n = 7, so then the number of degrees of freedom is df = n - 2 = 7 - 2 = 5
α = 0.05
Critical t value for df = 5 and α = 0.05 is +/- 2.5706 (Obtained using calculator. Screenshot attached)
Test statistic
Test statistic = 2.724
P-value
P-value corresponding to t = 2.724 and df = 5 is 0.0416 (Obtained using calculator)
Since p-value = 0.0416 < α = 0.05, we reject null hypothesis. Thus, there is a significant linear correlation between the variables
Regression equation
The equation of the regression line is:
y = -3 + 1.5*x
Add Answer to:
The table shows the number of years of education of parent and
the number of years...
A researcher wants to determine if the number of years of education that a person's father...
A researcher wants to determine if the number of years of education that a person's father has ("paeduc") is related to the number of years of education that the person has ("educ"). He uses simple linear regression to examine this question. The output from Excel is shown below. Regression Statistics Multiple R 0.527393938 R Square 0.278144366 Adjusted R Square 0.264776669 Standard Error 2.436826202 Observations 56 ANOVA df F Significance F 2.96139E-05 20.8072 Regression Residual Total SS MS 123.555701 123.5557 320.6585847...
If the data below represent the number of years of study and the wage earned by a sample of 10 women, calculate:
Explain briefly what is meant by linear correlation between two variables.
Use a graph if necessary. (4)
(b) If the data below represent the number of years of study and the wage
earned by a sample of 10 women, calculate:
i. the covariance of the two variables; (2)
ii. the coefficients of variation of the two variables; and (2)
iii. the variances of the two variables. (2) [10]
Person Years of study Wage (R'000s)
1
2
3
4
5
6...
correlations and linear regression education and income 3. Use the following data set and complete the table. (Inc...
correlations and linear regression education and income
3. Use the following data set and complete the table. (Income is the dependent variable and education is the independent variable) Education (Years) I x -* Yi- } (x; - x)(y;-)) (x; -x² Income ($1000) 15 46 13 17 58 46 13 10 40 63 15 18 11 9 11 15 45 12 50 16 9 14 48 58 14 16 50 11 a. Calculate x, y, and the standard deviations for both...
A sociologist is interested in predicting an income based on prior education level, with educatio...
PLEASE USE PREDICTION INTERVAL INSTEAD OF JUST USING EXCEL
A sociologist is interested in predicting an income based on prior education level, with education level defined as the number of years of formal schooling. The following table shows the collected data. 15 29 144 37 20 23 13 7 9 27 1411 Income (in thousand dollar) Education (in years) 10 14 9 3 17 12 8 11 4 15 68 For the simple linear regression model in Question 6, the...
3. The table below shows the regression output of a multiple regression model relating the beginn...
3. The table below shows the regression output of a multiple regression model relating the beginning salaries of employees in a given company to the following independent variables: Sex : an indicator variable (1=man and 0-woman) ducation years of schooling at the time of hire Experience number of months of previous work experience Source Regression Residual Total Df 4 8822,387,82 254,407 92 MS F-value 23.763,297 5,940,82423.35 46,151,118 Coefficient table Variable Constant Sex Education Experience Months t-value 10.94 6.02 3.22 2.16...
Regression Analysis Problem #1 The following table shows the sales (in $100,000) of a certain product as a function of...
Regression Analysis Problem #1 The following table shows the sales (in $100,000) of a certain product as a function of the past 10 months and the level of advertisement (in S1,000) for the corresponding months Sales 100 110 107 110 118 120 117122 120 125 Month 2 4 5 7 8 10 Advertisement 1.5 2.1 2,6 2.8 3.5 3.7 3.6 3.4 3.4 2.9 Part A: Considering a simple linear regression of sales vs, time (months), perform the following analysis manually,...
part b Jaaman une Regression Analysis Problem #L The following table shows the sales (in $100,000)...
part b
Jaaman une Regression Analysis Problem #L The following table shows the sales (in $100,000) of a certain product ma fnction of the pat 10 months and the level of advertisement (in $1,000) for the coresponding month 10 I 107 110 118 120 117 1221 120125 100 Sales 7 6 2.1 2.6 2,8 3.4 2.9 4 2 Month 10 3.4 3.5 3.7 36 Advertisement 1.5 Part A: Considering a simple linear regression of sales vs. time (months), perform ths...
Subject ID education memory 1 16 112 2 18 117 3 14 96 4 20 114...
Subject ID education memory 1 16 112 2 18 117 3 14 96 4 20 114 5 16 106 6 14 80 7 14 89 8 12 94 9 18 113 10 13 111 11 17 112 12 18 84 13 12 108 14 16 95 15 12 117 16 14 83 17 8 106 18 12 100 19 21 120 20 15 103 The data set for this question set (Tab Q1 in the Excel data file) comes from...
Observation Education (No. of years) Length of tenure in current employment (No. of years) Age (No....
Observation Education (No. of years) Length of tenure in current employment (No. of years) Age (No. of years) Annual income ($) 1 17 8 40 124,000 2 12 12 41 30,000 3 20 9 44 193,000 4 14 4 42 88,000 5 12 1 22 27,000 6 14 9 28 43,000 7 12 8 43 96,000 8 18 10 37 110,000 9 16 12 36 88,000 10 11 7 39 36,000 11 16 14 42 81,000 12 12 4 23...
Eclipse Engineering provides services of structural engineering. They just opened a new branch in...
Eclipse Engineering provides services of structural engineering. They just opened a new branch in Portland, OR. One of their products is called Structural Insulated Panels, or SIPs. It is a type of foam insulation that replaces typical wall and roof framing for residential or commercial buildings. Clients are billed a fixed fee for each project based on square footage of the building, square footage of the panel area, and number of panels. Depending on how long a project takes to...
A researcher wants to determine if the number of years of education that a person's father has ("paeduc") is related to the number of years of education that the person has ("educ"). He uses simple linear regression to examine this question. The output from Excel is shown below. Regression Statistics Multiple R 0.527393938 R Square 0.278144366 Adjusted R Square 0.264776669 Standard Error 2.436826202 Observations 56 ANOVA df F Significance F 2.96139E-05 20.8072 Regression Residual Total SS MS 123.555701 123.5557 320.6585847...
correlations and linear regression education and income
3. Use the following data set and complete the table. (Income is the dependent variable and education is the independent variable) Education (Years) I x -* Yi- } (x; - x)(y;-)) (x; -x² Income ($1000) 15 46 13 17 58 46 13 10 40 63 15 18 11 9 11 15 45 12 50 16 9 14 48 58 14 16 50 11 a. Calculate x, y, and the standard deviations for both...
PLEASE USE PREDICTION INTERVAL INSTEAD OF JUST USING EXCEL
A sociologist is interested in predicting an income based on prior education level, with education level defined as the number of years of formal schooling. The following table shows the collected data. 15 29 144 37 20 23 13 7 9 27 1411 Income (in thousand dollar) Education (in years) 10 14 9 3 17 12 8 11 4 15 68 For the simple linear regression model in Question 6, the...
3. The table below shows the regression output of a multiple regression model relating the beginning salaries of employees in a given company to the following independent variables: Sex : an indicator variable (1=man and 0-woman) ducation years of schooling at the time of hire Experience number of months of previous work experience Source Regression Residual Total Df 4 8822,387,82 254,407 92 MS F-value 23.763,297 5,940,82423.35 46,151,118 Coefficient table Variable Constant Sex Education Experience Months t-value 10.94 6.02 3.22 2.16...
Regression Analysis Problem #1 The following table shows the sales (in $100,000) of a certain product as a function of the past 10 months and the level of advertisement (in S1,000) for the corresponding months Sales 100 110 107 110 118 120 117122 120 125 Month 2 4 5 7 8 10 Advertisement 1.5 2.1 2,6 2.8 3.5 3.7 3.6 3.4 3.4 2.9 Part A: Considering a simple linear regression of sales vs, time (months), perform the following analysis manually,...
part b
Jaaman une Regression Analysis Problem #L The following table shows the sales (in $100,000) of a certain product ma fnction of the pat 10 months and the level of advertisement (in $1,000) for the coresponding month 10 I 107 110 118 120 117 1221 120125 100 Sales 7 6 2.1 2.6 2,8 3.4 2.9 4 2 Month 10 3.4 3.5 3.7 36 Advertisement 1.5 Part A: Considering a simple linear regression of sales vs. time (months), perform ths...
Eclipse Engineering provides services of structural engineering. They just opened a new branch in Portland, OR. One of their products is called Structural Insulated Panels, or SIPs. It is a type of foam insulation that replaces typical wall and roof framing for residential or commercial buildings. Clients are billed a fixed fee for each project based on square footage of the building, square footage of the panel area, and number of panels. Depending on how long a project takes to...
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