A business school is conducting a study to investigate whether a students’ scores on a placement test can be used to predict students’ starting salaries. Based on a random sample of 200 graduates of the business school, a 98 percent confidence interval for the slope of the linear regression line relating placement scores and starting salary is calculated to be (315,336). Assume the conditions for inference are met. Which of the following is a correct interpretation of the confidence interval? There is a 98 percent probability that the slope of the population regression line is between $315 per point and $336 per point. A Ninety-eight percent of the time, a 10-point increase in placement score will result in an average increase between $3,150 and $3,360 in starting salary. B We are 98 percent confident that a 10-point increase in placement score will result in a predicted increase in starting salary of between $3,150 and $3,360. C We are 98 percent confident that predicted starting salaries will be between $315,000 and $336,000. D We are 98 percent confident that the regression equation can be used to make accurate predictions for placement scores between 315 and 336. E
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 business school is conducting a study to investigate whether a students’ scores on a placement test can be used to predict students’ starting salaries. Based on a random sample of 200 graduates of the business school, a 98 percent confidence interval for the slope of the linear regression line relating placement scores and starting salary is calculated to be (315,336). Assume the conditions for inference are met.
Which of the following is a correct interpretation of the confidence interval?
-
There is a 98 percent probability that the slope of the population regression line is between $315 per point and $336 per point.
A -
Ninety-eight percent of the time, a 10-point increase in placement score will result in an average increase between $3,150 and $3,360 in starting salary.
B -
We are 98 percent confident that a 10-point increase in placement score will result in a predicted increase in starting salary of between $3,150 and $3,360.
C -
We are 98 percent confident that predicted starting salaries will be between $315,000 and $336,000.
D -
We are 98 percent confident that the regression equation can be used to make accurate predictions for placement scores between 315 and 336.
E
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