Problem 1: The regression below relates earnings to years of experience for a sample of 30 working adults. wage = 15.6 + 1.4*exp Predictor Coef SE Coef T Constant 15.6 2.38 6.55 Exp 1.40 .60 2.33 where wage equals hourly wage rate ($/hour) and exp equals years of work experience a)According to the above regression results, by how much does a year of experience increase the hourly wage rate? b)For a = .05, test the hypothesis that increases in experience are associated with increases in earnings. Clearly state the null and alternative hypotheses, show all relevant statistics for performing the test, and report the conclusion of your test. c)For a = .05 test the hypothesis that a 1year increase in experience increases the wage rate by more than $1/hour. Clearly state the null and alternative hypotheses, show all relevant statistics for performing the test, and report the conclusion of your test. d) What can you conclude from your answers to parts a-c? How can we explain these differences? e) For the wage regression coefficient, calculate a 95% confidence for its value and in 1 or 2 sentences describe its interpretation. Problem 2: Bike Sharing Data on the ISLE platform represent 731 days of recorded data with the following variable definitions: - workingday : if day is neither weekend nor holiday is 1, otherwise is 0. - temp : Normalized temperature in Celsius. - atemp: Normalized feeling temperature in Celsius. - hum: Normalized humidity. - windspeed: Normalized wind speed. - count: count of total bike rentals a) Create a scatterplot in ISLE that shows the relationship between temperature (independent variable) and count (dependent variable). Does a pattern exist? b) What is the least squares linear regression equation to model this relationship? How do we interpret this coefficient in the context of the problem? Paste your ISLE output. c) What information should we use to make inferences about ? For α=.05, use ISLE to test whether each one degree increase in temperature increases the count of rentals by more than 6000. Clearly, state the null and alternative hypotheses, test statistic, and the conclusion of the test. d) In terms of R2, which of the four weather variables is the worst predictor of bike rentals? Produce a scatterplot of each comparison.
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.
Problem 1: The regression below relates earnings to years of experience for a sample of 30 working adults.
wage = 15.6 + 1.4*exp
Predictor Coef SE Coef T
Constant 15.6 2.38 6.55
Exp 1.40 .60 2.33
where wage equals hourly wage rate ($/hour) and exp equals years of work experience
a)According to the above regression results, by how much does a year of experience increase the hourly wage rate?
b)For a = .05, test the hypothesis that increases in experience are associated with increases in earnings. Clearly state the null and alternative hypotheses, show all relevant statistics for performing the test, and report the conclusion of your test.
c)For a = .05 test the hypothesis that a 1year increase in experience increases the wage rate by more than $1/hour. Clearly state the null and alternative hypotheses, show all relevant statistics for performing the test, and report the conclusion of your test.
d) What can you conclude from your answers to parts a-c? How can we explain these differences?
e) For the wage regression coefficient, calculate a 95% confidence for its value and in 1 or 2 sentences describe its interpretation.
Problem 2: Bike Sharing Data on the ISLE platform represent 731 days of recorded data with the following variable definitions:
- workingday : if day is neither weekend nor holiday is 1, otherwise is 0.
- - temp : Normalized temperature in Celsius.
- - atemp: Normalized feeling temperature in Celsius.
- - hum: Normalized humidity.
- - windspeed: Normalized wind speed.
- - count: count of total bike rentals
a) Create a
b) What is the least squares linear regression equation to model this relationship? How do we interpret this coefficient in the context of the problem? Paste your ISLE output.
c) What information should we use to make inferences about ? For α=.05, use ISLE to test whether each one degree increase in temperature increases the count of rentals by more than 6000. Clearly, state the null and alternative hypotheses, test statistic, and the conclusion of the test.
d) In terms of R2, which of the four weather variables is the worst predictor of bike rentals? Produce a scatterplot of each comparison.
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