Variable Y represents the profit (in thousand of dollars ) of an indoor heating repairs firm in a small town , over four consecutive months. The variable X1 represents the average outside temperature for the month, and the variable X2 represents the average number of daily customer complements(positive) or complaints(negative). For a month in which X2 is positive there were more complements than complaints but for a month in which X2 is negative there were more complaints than compliments. Using the information about variables Month X1 X2 Y NOVEMBER -5 5 11 DECEMBER -4 4 11 JANUARY -1 1 8 FEBRUARY 2 -3 2 i. Determine by a matrix method the equation of the line of regression for Y on X1 and X2. ii. Use your results in i. to predict the expected profit of the firm in a month where the average outside temperature was -2 degrees and the average number of daily customers compliment was 3.
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.
Variable Y represents the profit (in thousand of dollars ) of an indoor heating repairs firm in a
small town , over four consecutive months. The variable X1 represents the average outside
temperature for the month, and the variable X2 represents the average number of daily
customer complements(positive) or complaints(negative). For a month in which X2 is positive
there were more complements than complaints but for a month in which X2 is negative there
were more complaints than compliments. Using the information about variables
Month X1 X2 Y
NOVEMBER -5 5 11
DECEMBER -4 4 11
JANUARY -1 1 8
FEBRUARY 2 -3 2
i. Determine by a matrix method the equation of the line of regression for Y on X1 and
X2.
ii. Use your results in i. to predict the expected profit of the firm in a month where the
average outside temperature was -2 degrees and the average number of daily
customers compliment was 3.
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