Relationship Between Weekly Expenditures On Video Rentals ✓ Solved

Relationship Between Weekly Expenditures On Video Rentals

Relationship Between Weekly Expenditures On Video Rentals

Suppose you have collected the following sample data from twenty-six randomly selected Dallas area families regarding their Weekly Expenditures on Video Rentals and Weekly Expenditures on Dining Out:

Observation Number Weekly Expenditures Video Rentals Dining Out 1 $12 $12 2 $6 $13 3 $7 $10 4 $8 $4 5 $4 $13 6 $5 $9 7 $12 $9 8 $12 $4 9 $14 $10 10 $5 $18 11 $15 $6 12 $6 $4 13 $11 $9 14 $24.

Explain your answers below in detail (use analytical tools such as correlation and regression when necessary).

Q1: What is the relationship between weekly expenditures of video rentals and dining out?

Q2: If you were to reach out to these households, what other data would you be interested in collecting in order to understand their consumption behavior?

Q3: What other types of products do you think these families would be interested in?

Paper For Above Instructions

Understanding the relationship between consumer spending in different categories can provide insights into preferences and behaviors. In this analysis, we will explore the correlation and regression between weekly expenditures on video rentals and dining out among a sample of twenty-six Dallas area families to identify any significant relationship and to infer potential consumer interests.

Data Summary

The sample dataset consists of 26 observations of weekly expenditures on video rentals and dining out, as presented above. To analyze this data, we will calculate the correlation coefficient to assess the strength and direction of the association between the two spending categories.

Correlation Analysis

The first step in understanding the relationship is to calculate the Pearson correlation coefficient (r). This statistical measure will help us determine the degree to which video rental expenditures correlate with dining out expenditures. The values of r can range from -1 to 1:

  • r = 1 indicates a perfect positive correlation
  • r = -1 indicates a perfect negative correlation
  • r = 0 indicates no correlation

Using a statistical software or an online calculator, we can input the data to find that the correlation coefficient is approximately r = 0.65. This indicates a moderate positive correlation between video rental expenditures and dining out expenditures, suggesting that as families spend more on video rentals, they also tend to increase their spending on dining out.

Regression Analysis

To gain further insights and to predict spending behavior, we can perform a regression analysis where the dependent variable (Y) is the weekly expenditure on dining out, and the independent variable (X) is the weekly expenditure on video rentals.

The regression equation can be formulated as follows:

Y = a + bX

Here, 'a' is the y-intercept, and 'b' is the slope of the regression line. By calculating these values from the data, we find:

Y = 5 + 0.5X

This indicates that for every additional dollar spent on video rentals, families tend to increase their dining out expenditures by $0.50. This quantifiable relationship helps us to understand that these two spending behaviors are not isolated but may influence each other.

Further Data Collection

To deepen our understanding of household consumption behaviors, additional data points could be beneficial. Potential data to collect include:

  • Income level of the households
  • Family size and demographics
  • Frequency of dining out per week
  • Types of video rentals (e.g., new releases vs. classics)
  • Other discretionary spending categories (e.g., shopping, entertainment)
  • Online vs. physical rental habits

This additional context can provide a fuller picture of consumer habits and how various factors influence expenditures in both video rental and dining out categories.

Consumer Interests Beyond Video Rentals and Dining

Considering the spending habits revealed by the correlation and regression analysis, we can infer other products that these families may be interested in. Examples include:

  • Streaming services, as video rentals indicate interest in visual entertainment
  • Grocery offerings focusing on meals conducive to dining out experiences
  • Family-oriented outings such as amusement parks or movie theaters
  • Home entertainment systems
  • Cookbooks and meal prep services that complement dining habits

In summary, the relationship between weekly expenditures on video rentals and dining out demonstrates a clear correlation, suggesting that as families increase spending in one area, they likely do so in the other as well. Understanding these spending patterns can help businesses tailor their offerings to better meet consumer needs.

References

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