Question

Data was collected on the amount of food (in grams) served at two restaurants and the price paid for the meal. The regression line for the data appears on the first plot. The second plot shows the regression analysis conducted when the data is analyzed separately for each of the two restaurants. Which of the following statements best describes the relationship between the variables?

a. The correlation between amount of food served and price is very strong within each restaurant, but seems weak when both restaurants are combined.
b. The correlation between amount of food served and price is strong.
c. The correlation between amount of food served and price is weak within each restaurant, but seems strong when both restaurants are combined.
d. The correlation between amount of food served and price is weak.

Answer 1

The best description of the relationship between the amount of food served and the price paid for the meal is that there is a strong correlation within each restaurant but a weak correlation when data from both restaurants are combined.

Step-by-step explanation:

The student is analyzing the relationship between two variables: the amount of food served (independent variable) and the price paid for the meal (dependent variable). The scatter plots mentioned in the question, which are not provided here, suggest different patterns of correlation when the data from two restaurants is combined and when analyzed separately.

Overall, the correct answer to the student's question based on the information given would be (a) The correlation between amount of food served and price is very strong within each restaurant, but seems weak when both restaurants are combined. This implies that each restaurant individually has a consistent pattern where more food relates to a higher price, whereas the combined data might show a more scattered relationship, possibly due to different pricing strategies at the two establishments.

To confirm these findings, one would typically:

• Draw a scatter plot.
• Calculate a least-squares regression line: ý = a + bx.
• Find the correlation coefficient to quantify the strength of the relationship.
• Interpret whether the correlation is significant.

Answer 2

Option A, The correlation between amount of food served and price is very strong within each restaurant, but seems weak when both restaurants are combined.

Step-by-step explanation:

The graphs for this question are provided in the attachment

Solution -

Graph I - the data points in the graph I do not follow any best fit curve or trendline. This indicates that data is not correlated.

Graph -II In graph II, apart from few outliners majority of data points lie on the best fist curve or the trendline.

Hence, the relation between the two variables i.e food served and price is strong.

Option A fits well for our answer hence it is the correct answer