Question

You are in charge of pricing for a California wine company. Because nearly 90% of U.S. wines are produced in California, you think that California wines might be perceived differently from those produced in other states, thus affecting the price. You decide to see how both wine rating and whether or not the wine is from California affect the pricing of wines in the U.S.

Based on the model you estimated, at what rating do California wines become more expensive than wines from other states? Round your answers to 2 decimal places.

Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations 0.4867 0.2368 0.2368 21.7452 62139 ANOVA MS Significance F Regression Residual Total 3 91,18,501.87 30,39,500.62 6,427.97 0.00 62135 293,80,894.86 62138 384,99,396.73 472.86 Coefficients 215.62 2.78 -67.33 0.86 Standard Error 4.72 0.05 5.37 0.06 P-value 0.00 0.00 0.00 0.00 Lower 95% Upper 95% 206.37 2.88 56.80 0.98 tstat Intercept Rating California -45.69 51.88 12.54 14.06 224.87 2.67 77.85 0.74 ating * California

Answer 1

In general the equation is:

Price, P = -215.62 + R * 2.78 - C * 67.33 + 0.86 * (R*C)

Now when Wine is not from California, C = 0

So, P₁ = -215.62 + 2.78 * R

When Wine is from California, C = 1

P₂ = -282.95 + 3.64 * R

Let's find value of R for which P₂ = P₁

-282.95 + 3.64 * R = -215.62 +2.78 * R

-282.95 + 215.62 = 2.78R - 3.64R

-67.33 = -0.86*R

0.86R = 67.33

R = 78.2907

For P2 > P1

Any value of R above 78.2907 means P2 > P1

So For R = 78.2908, P2 > P1

For R = 78.2907, P1 = P2 = 2.028

For R = 78.2908, P1 = 2.028, P2 = 2.029

So R = 78.2908 or approximately 78.3, California Wines become expensive than Wines from Other states