Math Problem Statement
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.05 level of significance.
Critical Values of the Pearson Correlation Coefficient
Average Temperatures and Snow Accumulations Average Temperature (℉) 39 29 20 44 45 15 34 25 28 42 Snow Accumulation (in.) 7 19 22 10 14 29 22 19 20 5
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Pearson Correlation Coefficient
Statistical Significance Testing
Formulas
Regression Line: yˆ = b0 + b1x
Slope (b1): b1 = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
Intercept (b0): b0 = ȳ - b1x̄
Pearson Correlation Coefficient: r = (nΣxy - ΣxΣy) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]
Theorems
Linear Regression Theorem
Pearson Correlation Coefficient Significance Test
Suitable Grade Level
Grades 10-12
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