a. In interpreting this case, the residuals seem to be relatively small and do not show a clear pattern, suggesting a reasonably strong negative correlation based on a negative slope (-115).
b. The slope (-115) shows that for each dollar increase in the price per pound of tomatoes, the store sells 115 fewer tomatoes per week.
The y-intercept (273) shows that if the tomatoes were given away for free, the store would sell 273 tomatoes per week.
How the interpretation is conducted:
a) The residuals in the table represent the difference between the observed values (actual number of tomatoes sold) and the predicted values (number of tomatoes sold according to the model). If the residuals are small and randomly distributed around zero, it indicates a strong correlation. However, if the residuals show a pattern or are not close to zero, it indicates a weaker correlation.
b) Given the equation of the line as y = -115x + 273:
The slope (-115) represents the rate at which the number of tomatoes sold decreases for each dollar increase in the price per pound.
The y-intercept (273) represents the number of tomatoes that would be sold if the price per pound were $0.
Thus, our interpretation assumes that the relationship between price and quantity sold is linear over the entire range, which may be outside reality.
Complete Question:
The table shows the price x (in dollars per pound) of tomatoes at a store and the weekly number y of tomatoes sold.
The equation y = -115x + 273 models the data. The residuals are shown in the table.
X y Residual
1.24 128 -2.4
1.56 98 4.4
1.30 122 -1.5
1.12 140 -4.2
1.96 48 0.4
1.64 82 2
1.16 142 -2.4
1.40 114 2.4
a. Interpret the strength and direction of the correlation.
b. Interpret the slope and y-intercept of the line of fit in this situation.