Summary statistics for data relating the latitude 1°North2and average January low temperature 1°F2 for 55 largeU.S. cities are given below. A scatterplot suggests a linearmodel is appropriate.a) Write the equation of the least squares regressionline that predicts a U.S. city’s average January lowtemperature based on its latitude.b) Interpret the slope in context.c) Do you think the y-intercept is meaningful? Explain.d) For a certain city the residual is -4.2°. Explain whatthat means. Latitude Avg Jan LowMean 39.02 26.44StDev 5.42 13.49Correlation -0.848
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.
Summary statistics for data relating the latitude 1°North2
and average January low temperature 1°F2 for 55 large
U.S. cities are given below. A
model is appropriate.a) Write the equation of the least squares regression
line that predicts a U.S. city’s average January low
temperature based on its latitude.
b) Interpret the slope in context.
c) Do you think the y-intercept is meaningful? Explain.
d) For a certain city the residual is -4.2°. Explain what
that means.
Latitude Avg Jan Low
Mean 39.02 26.44
StDev 5.42 13.49
Correlation -0.848
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