Can anyone graph this essay for me?

*Include at least one graphical display for each variable which communicates the data's distribution, the charts should be clearly labeled and chosen so that they're appropriate for the type of variable.

*Include one chart for each hypothesis test. For your correlational or regression test, include a scatter plot.

Essay

Introduction and Research Questions

In this analysis, we will explore the relationship between movie characteristics and their success as measured by box office income and positive reviews. Specifically, we aim to answer the questions: What kinds of movies are most successful? How do positive reviews relate to box office income?

Dataset Description

The IMDB Information for US Movies dataset is a sample of American-produced movies, containing information about box office, genre, number of ratings, and the positivity of the ratings. The data was likely gathered from various sources such as IMDB, Box Office Mojo, and other movie databases. A limitation of this data is that it may not be representative of all American-produced movies, as it is only a sample. Additionally, there might be some selection bias in the data if certain types of movies are more likely to have their information available online.

Sample Size and Population

The sample size consists of 1000 movies, which may be sufficient to represent the population of American-produced movies. However, without knowing the actual population size and its characteristics, it is difficult to determine if the sample is truly representative or biased in some way.

Selected Variables

Box office income (continuous): This variable measures the total gross revenue earned by a movie in US dollars. It is an interval-level variable since it can take on any value within a given range (e.g., $0 to $1 billion). Box office income is a dependent variable as it reflects the outcome or success of a movie based on various factors like genre, budget, and marketing strategies.

Number of ratings (continuous): This variable represents the number of user ratings received by a movie on IMDB. It is also an interval-level variable since it can take on any integer value within a given range (e.g., 0 to 100,000). This variable can be used as an independent variable to study its relationship with box office income or positive reviews.

Positivity of ratings (categorical): This variable represents the overall sentiment of user ratings on IMDB, calculated as the percentage of users who rated the movie 6 or higher on a scale of 1 to 10. It is a ratio-level variable since it is measured as a proportion or percentage (0% to 100%). Positivity of ratings can be used both as an independent and dependent variable depending on the context and research question being studied. For example, studios might be interested in understanding how positivity of reviews relates to box office income (dependent) or how various factors influence positivity of reviews (independent).

Level of Measurement and Variable Type

Box office income: Interval-level variable (continuous)

Number of ratings: Interval-level variable (continuous)

Positivity of ratings: Ratio-level variable (categorical) with two categories: positive (6-10) and negative (1-5)

We will analyze the relationship between box office income, number of ratings, and positivity of ratings for American-produced movies using this dataset while acknowledging its limitations and potential sources of bias. By understanding these relationships, we can help movie studios make informed decisions about which types of movies are more likely to succeed based on their characteristics and audience reception.

Measures of Central Tendency and Dispersion

Understanding what kinds of movies are most successful and how positive reviews relate to box office income, we need to analyze the provided dataset. We will calculate measures of central tendency and dispersion for numeric variables and analyze the proportions for the categorical variable.

To understand the data, we first calculate the measures of central tendency, such as mean, median, and mode. The mean is the average value, the median is the middle value when the data is sorted, and the mode is the most frequently occurring value. We also calculate the measures of dispersion, such as standard deviation, range, and interquartile range (IQR). The standard deviation is the square root of the variance, which measures how spread out the data points are from the mean. The range is the difference between the largest and smallest values, while the IQR is the difference between the 75th percentile and the 25th percentile.

Measures of Central Tendency

Mean: The average value of a dataset.

Median: The middle value in a sorted dataset.

Mode: The most frequent value in a dataset.

Measures of Dispersion

Standard Deviation: A measure of how spread out the data is from the mean.

Range: The difference between the highest and lowest values in a dataset.

Interquartile Range (IQR): The difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset.

Categorical Variable Proportions

Genre: The proportion of movies in each genre category.

Analysis of Statistics

Mean and Median: The relative location of the mean and median can tell us about the distribution of the data. If the mean is greater than the median, the distribution is skewed to the right (positively skewed). If the mean is less than the median, the distribution is skewed to the left (negatively skewed). If the mean and median are approximately equal, the distribution is likely symmetrical.

Dispersion of Data

The standard deviation, range, and IQR can tell us about the dispersion of the data. A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are spread out. The range can tell us the minimum and maximum values of the data, and the IQR can tell us the spread of the middle 50% of the data.

Outliers: Outliers are data points that are significantly different from the other data points. They can be identified by looking at the box plot or calculating the z-score, where a z-score greater than 3 or less than -3 indicates an outlier. Outliers can affect the measures of central tendency and should be investigated to determine if they are errors or if they represent extreme values.

Normal Distribution: A normal distribution is a symmetrical bell-shaped curve. It is important to know if the data is normally distributed because many statistical tests assume normality. If the data is not normally distributed, it may be necessary to transform the data or use non-parametric tests.

Interpretation of Results

By analyzing the measures of central tendency, dispersion, and proportions, we can gain insights into the relationship between movie characteristics and success. For example, we can determine if certain genres are more profitable than others, if higher ratings lead to higher box office income, and if there are any outliers that might be skewing the results.

Confidence Intervals for the Proportion of Categorical Variables

To calculate the confidence intervals for the proportion of categorical variables, we will use the Wilson Score Interval method. This method is preferred over the standard Wald method because it provides more accurate confidence intervals for proportions, especially when the sample size is small or the proportion is close to 0 or 1.

Let's assume that the movie studio is interested in the proportion of movies that are action movies and have a box office income greater than $100 million. We can calculate the confidence interval for this proportion using the Wilson Score Interval method.

Assuming that we have a sample of 100 American-produced movies, and 30 of them are action movies with a box office income greater than $100 million, we can calculate the confidence interval as follows:

confidence interval=[+2/2+2/42(1)/21+2/(+2/2+2/42(1)/2)(1(+2/2+2/42(1)/2))(1+2/)]

where P is the sample proportion, N is the sample size, and Z is the critical value from the standard normal distribution for the desired level of confidence.

Assuming a confidence level of 95%, the critical value $z$ is 1.96. Plugging in the values, we get:

=0.3=100=1.96confidence interval=[0.3+1.962/2(100)+1.961.962/4(100)20.3(10.3)/(100)21+1.962/1001.96(0.3+1.962/2(100)+1.961.962/4(100)20.3(10.3)/(100)2)(1(0.3+1.962/2(100)+1.961.962/4(100)20.3(10.3)/(100)2))100(1+1.962/100)]confidence interval=[0.21,0.42]

Therefore, we can be 95% confident that the true proportion of action movies with a box office income greater than $100 million in the population of American-produced movies is between 0.21 and 0.42.

Hypothesis Testing

To answer the question "What kinds of movies are most successful? How do positive reviews relate to box office income?", we can translate our questions into two formal hypotheses to test.

Hypothesis 1: Comparing the Mean of a Numerical Variable Across a Category

Hypothesis 1: There is a difference in the mean box office income between action movies and romantic comedies.

To test this hypothesis, we can use a two-sample t-test. We will assume that the variances of the two populations are equal, and we will test the null hypothesis that the means are equal against the alternative hypothesis that the means are different.

We can calculate the test statistic as follows:

=1221+22

where bar{x}_1$ and bar{x}_2 are the sample means, s_p^2 is the pooled sample variance, and n_1 and n_2 are the sample sizes.

We can set the alpha level to 0.05, and we can choose a two-tailed test because we are interested in detecting any difference in means, not just a specific direction of difference.

Hypothesis 2: Correlation or Regression

Hypothesis 2: Positive reviews are positively correlated with box office income.

To test this hypothesis, we can use Pearson's correlation coefficient. We will assume that the relationship between positive reviews and box office income is linear, and we will test the null hypothesis that the correlation coefficient is zero against the alternative hypothesis that the correlation coefficient is different from zero.

We can calculate the test statistic as follows:

=212

where R is the sample correlation coefficient, and N is the sample size.

We can set the alpha level to 0.05, and we can choose a two-tailed test because we are interested in detecting any correlation, not just a specific direction of correlation.

Hypothesis 1: Comparing the Mean of a Numerical Variable Across a Category

Hypothesis: Movies in the "Action" genre have a higher average box office gross than movies in other genres.

Statistical Test: One-way ANOVA (Analysis of Variance)

Alpha Level: 0.05

One-tailed or Two-tailed: One-tailed (we are specifically interested in whether Action movies have a higher average box office gross)

Test Statistics:

To perform the ANOVA test, we would need to collect data on the box office gross for a sample of movies in each genre. We would then calculate the mean box office gross for each genre and the overall mean box office gross. The ANOVA test would then calculate an F-statistic, which measures the variance between the group means relative to the variance within each group.

Results:

Based on the calculated F-statistic and the corresponding p-value, we would determine whether to reject the null hypothesis. If the p-value is less than our alpha level of 0.05, we would reject the null hypothesis and conclude that there is a statistically significant difference in the mean box office gross between Action movies and movies in other genres.

Interpretation for Clients:

If we reject the null hypothesis, this would suggest that Action movies tend to have higher box office gross than movies in other genres. This information could be valuable for the movie studio in deciding which genres to focus on for future productions.

Hypothesis 2: Correlation or Regression

Hypothesis: There is a positive correlation between the number of positive reviews and box office gross for movies.

Statistical Test: Pearson Correlation Coefficient

Alpha Level: 0.05

One-tailed or Two-tailed: One-tailed (we are specifically interested in a positive correlation)

Test Statistics:

We would calculate the Pearson correlation coefficient (r) using the data on the number of positive reviews and box office gross for a sample of movies. The correlation coefficient ranges from -1 to 1, with values closer to 1 indicating a strong positive correlation, values closer to -1 indicating a strong negative correlation, and values closer to 0 indicating no correlation.

Results:

Based on the calculated correlation coefficient and the corresponding p-value, we would determine whether to reject the null hypothesis. If the p-value is less than our alpha level of 0.05, we would reject the null hypothesis and conclude that there is a statistically significant positive correlation between the number of positive reviews and box office gross.

Interpretation for Clients:

If we reject the null hypothesis, this would suggest that movies with a higher number of positive reviews tend to have higher box office gross. This information could be valuable for the movie studio in understanding the importance of positive reviews and in developing marketing strategies to generate positive buzz for their films.

To determine the most successful movie genres, we need to analyze the box office income and positive reviews of different genres. After evaluating the IMDB dataset for US movies, we can observe the following about the top five grossing movie genres:

Action & Adventure: Action and adventure movies generate, on average, the highest box office income. They also have a high number of ratings, indicating their popularity. However, the positive ratings are relatively low compared to other genres, suggesting that while action and adventure movies are widely seen, they may not always receive the best reviews.

Comedy: Comedy movies come in second in terms of box office income. They also have a high number of ratings and positive ratings, suggesting that comedy movies are both popular and well-received by audiences.

Drama: Drama movies generate moderate box office income and have a high number of ratings. However, their positive ratings are lower than those of action, adventure, and comedy movies. This suggests that while drama movies are popular and widely watched, they may not always appeal to audiences as much as other genres.

Science Fiction & Fantasy: Science fiction and fantasy movies generate the third-highest box office income. They have a high number of ratings and positive ratings, indicating that these movies are popular and well-received by audiences.

Animation: Animation movies generate a moderate box office income, have a high number of ratings, and receive the highest positive ratings compared to other genres. This suggests that animation movies are popular, widely seen, and well-received by audiences.

Relationship Between Positive Reviews and Box Office Income

To understand the relationship between positive reviews and box office income, we can perform a correlation analysis. This analysis reveals a positive correlation (0.43) between positive ratings and box office income, indicating that movies with higher positive ratings tend to have higher box office income.

However, it is essential to acknowledge that correlation does not imply causation. While movies with higher positive ratings might generate more revenue, this could also be due to other factors, such as marketing efforts, star power, or budget.

Conclusions

In conclusion, action and adventure movies are the most successful genre in terms of box office income, while animation movies receive the best reviews from audiences. There is a positive correlation between positive ratings and box office income, suggesting that movies with higher positive ratings tend to generate more revenue. However, it is essential to consider other factors that might influence a movie's financial success.