Question

Your friend Stephano claims that he can predict the sales at your new ice cream store using a process that he calls "temporal temperature intuition." Your sales for the first four days are $1000, $1100, $1600, and $1100. Stephano's predictions for those four days were $1100, $1500, $1500, and $1300. Compute his R-squared in order to determine whether his model is GOOD or NO GOOD.

Answer 1

Stephano's R-squared value for predicting ice cream sales is calculated to be 0.58, which does not signify a strong predictive model, thus his method might be labeled as NO GOOD.

Step-by-step explanation:

To compute Stephano's R-squared, which determines the goodness of fit of his predictions for the ice cream store sales, we need to follow several steps. First, compute the total sum of squares (SST), which measures the total variance in the observed data. Then, compute the sum of squares of the regression (SSR), which measures the variance explained by the prediction. Finally, calculate the sum of squares of the residuals (SSE), which measures the variance that is not explained by the prediction.

The formula for R-squared (R2) is R2 = 1 - (SSE / SST). To find SST, SSR, and SSE, we use the actual sales and predicted sales:

• Calculate the mean of the actual sales: (1000 + 1100 + 1600 + 1100) / 4 = 1100.
• Calculate SST: [(1000 - 1100)2 + (1100 - 1100)2 + (1600 - 1100)2 + (1100 - 1100)2] = 5002 + 0 + 5002 + 0 = 500000.
• Calculate SSE: [(1000 - 1100)2 + (1100 - 1500)2 + (1600 - 1500)2 + (1100 - 1300)2] = 1002 + 4002 + 1002 + 2002 = 10000 + 160000 + 10000 + 40000 = 210000.
• Compute R2: 1 - (210000/500000) = 1 - 0.42 = 0.58.

An R2 value of 0.58 does not indicate a very strong fit between Stephano's predictions and the actual sales data. Therefore, his prediction model might be considered NO GOOD.