This hypothesis testing is to try to understand if there is correlation between the average scores given by wine spectator and the average prices for wineries in Napa.
Step 1 Define my Hypothesis
Ho: There is no correlation between WS Score and Price for Napa Wines
H1: there is a correlation between WS Score and price for Napa wines
Step 2 run the regression Analysis
The regression equation is
Napa Price = - 2040 + 23.5 Napa Score
Predictor Coef StDev T P
Constant -2040.3 318.8 -6.40 0.000
Napa Sco 23.488 3.557 6.60 0.000
S = 33.21 R-Sq = 57.7% R-Sq(adj) = 56.4%
Analysis of Variance
Source DF SS MS F P
Regression 1 48111 48111 43.61 0.000
Residual Error 32 35301 1103
Total 33 83412
Obs Napa Sco Napa Pri Fit StDev Fit Residual St Resid
21 92.5 68.33 132.36 11.72 -64.03 -2.06R
29 94.4 275.00 176.99 17.92 98.01 3.51RX
R denotes an observation with a large standardized residual
X denotes an observation whose X value gives it large influence.
Step 3 Explain the results
We Reject the null hypothesis.
The P-value for Napa Score is <.05 which leads us to conclude that Score is a good predictor of Price and there is a correlation between Score and Price
The R-sq(adj) value is high, which tells us that the regression equation explains a high percentage of the variation in the process (close 60%).
Step 4 Conclusion
It looks like that score is a strong predictor of a price for Napa wines.
Note:"Correlation does not imply causation"