Suppose a gas station monitors how many bags of ice they sell along with the maximum daily temperature for 100 days. A gas station data analyst plots the data in a scatter plot with temperature, in °F, on the horizontal axis and the number of bags of ice sold on the vertical axis. She calculates a linear correlation coefficient of r = 0.9972. The mean temperature is 83.8959 °F with a standard deviation of 11.2921 °F. The mean number of ice bags sold is 70.3873 with a standard deviation of 27.8913. Determine the slope, b, and the intercept, a, of the least-squares regression line for this dataset, precise to two decimal places. b = a = Predict how many bags of ice are sold, ŷ, to the nearest whole number, when the temperature is 87.00°F.
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.
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