Although the event may seem startling to their students,119 statistics teachers participated in a fun run. Beforethe run, each person was asked to guess what his/her timewould be (in seconds). After the run, the actual times were plotted against the teachers’ guesses, and the as-sumptions for inference appeared to be reasonable. Here is the regression output:Dependent Variable: actualtimeR-squared = 75.01%s = 278.1940Variable Coefficient Se(coeff) t-ratio P-ValueIntercept 156.3777 79.3023 1.9719 0.051guess 0.887006 0.04734 18.739 60.0001a) Does this output provide evidence of an associationbetween guessed time and actual time? Explain. b) Assuming these 119 teachers represent a representa-tive sample from a larger population who might par-ticipate in such a run, construct and interpret a 95% confidence interval for the slope of the regression linefor that population.c) Does the interval you constructed in part b) supportyour conclusion in part a)? Explain.

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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.