Final answer:
Using the linear equation derived from the regression line, the prediction for the number of t-shirts sold at $13 is approximately 18. Since sales of half a shirt are not reasonable, the prediction would round to the nearest whole number, suggesting that 18 t-shirts is the most accurate prediction.
Step-by-step explanation:
The question is asking for a prediction of t-shirt sales for $13 based on a provided regression line that fits the data points. The data shows a list of prices (x) and the corresponding number of t-shirts sold (y). A trend line through the points (10, 26) and (14, 16) indicates a linear relationship between the price and the number sold.
To predict the number of t-shirts sold at $13, we need to use the equation of the trend line, which is derived from the two points given. First, we find the slope (m) of the line: m = (y2-y1) / (x2-x1) = (16-26) / (14-10) = -10 / 4 = -2.5.
Now we can use one of the points to find the y-intercept (b), using the formula y = mx+b:
26 = -2.5(10) + b
b = 26 + 25
b = 51.
So, the equation of the trend line is y = -2.5x + 51. To predict the number of t-shirts that would be sold at $13, substitute x with 13:
y = -2.5(13) + 51
y = -32.5 + 51
y = 18.5.
Since we cannot sell half a t-shirt, the reasonable prediction would be selling approximately 18 t-shirts. Therefore, the 15 t-shirts option would be conservative, while 18 t-shirts is a closer estimate according to the prediction. In conclusion, based on the results of the t-shirt sales analysis shown by the regression calculator, a price of $13 each is a reasonable prediction for selling 18 t-shirts, making it the correct option.