Consider the following table showing January mean monthly precipitation and mean
ID: 3060482 • Letter: C
Question
Consider the following table showing January mean monthly precipitation and mean daily high temperature for 10 cities.
1.6
Construct a scatter diagram and based on visual inspection draw the fest fit line bye eye.
Compare r and r2.
For this case do you believe that the best fit line gives reliable predictions outside the range of the data on the scatter diagram?
Predictions based on the vest fir line are reliable because the value of r2 is very small.
Predictions based on the vest fir line are NOT reliable because the value of r2 is very small.
City January high temperature January precipitaion 1 53 2.3 2 87 0.2 3 35 1.7 4 54 5.2 5 43 2.1 6 20 3.9 7 29 1.8 8 53 3.4 9 46 2.0 10 331.6
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: January precipitaion
Independent Variable: January high temperature
January precipitaion = 3.4591503 - 0.022939299 January high temperature
Sample size: 10
R (correlation coefficient) = -0.30388975
R-sq = 0.092348978
Estimate of error standard deviation: 1.4161409
Parameter estimates:
Analysis of variance table for regression model:
Hence,
r = -0.304
r2 = 0.092
Predictions based on the vest fir line are NOT reliable because the value of r2 is very small.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 3.4591503 1.235794 0 8 2.7991318 0.0232 Slope -0.022939299 0.02542603 0 8 -0.90219744 0.3933