Question

You have the following data on the number of dishes of ice cream that 4 people eat in a month:

Alice: 12
Baruk: 12
Carlos: 6
Daria: 14
You create two categories based on gender: Daria and Alice in one, and Carlos and Baruk in the other. You make predictions based on these categories. How much of the variation can you explain based on these categories, i.e. what's your R-squared? Write your answer as a number between 0 and 1 to the hundredths place (like this: 0.XX). Write only your final answer

Answer 1

The R-squared value, which measures the proportion of the total variation in the dependent variable that can be explained by the independent variable, is 0.5.Therefore, the R-squared value is 0.5.

Step-by-step explanation:

R-squared, or the coefficient of determination, measures the proportion of the total variation in the dependent variable (number of dishes of ice cream eaten) that can be explained by the independent variable (categories based on gender). To calculate R-squared, you need to first calculate the total sum of squares (SST), the explained sum of squares (SSE), and the residual sum of squares (SSR). Then, use the formula R-squared = 1 - (SSR/SST). In this case:

SST = (12-9)^2 + (12-9)^2 + (6-9)^2 + (14-9)^2
= 9 + 9 + 9 + 25
= 52

SSE = (12-9)^2 + (12-9)^2 + (6-9)^2 + (14-9)^2/2
= 9 + 9 + 9 + 25/2
= 52/2
= 26

SSR = SST - SSE
= 52 - 26
= 26

R-squared = 1 - (SSR/SST)
= 1 - (26/52)
= 1 - 0.5
= 0.5

Therefore, the R-squared value is 0.5.