AFE135 Business Data Analysis

The frequency table and the histogram for the weekly food expenditure as per the class intervals described in part (b) are given as follows:

Table 4

The average weekly take home pay was found to be $50.58 for a typical participant. The variance was 56481.72 and the standard deviation was 237.65 which gives the extent of spread of the data around the mean value. Fifty percent of the people earned at least $465 as suggested by the median value. Seventy five percent of the people earn at least $313 per week on an average as suggested from the first quartile value and twenty five percent people at least earn $680.5 per week on an average as suggested from the third quartile. The minimum weekly take home pay was found to be $105 and the maximum take home pay per week was $1090.          

Table 5

The average weekly expenditure of food was found to be $197.99 for a typical participant. The variance was 6848.11 and the standard deviation was 82.75 which gives the extent of spread of the data around the mean value. Fifty percent of the people spent at least $190.87 on food as suggested by the median value. Seventy five percent of the people spent at least $128.73 per week on an average on food as suggested from the first quartile value and twenty five percent people at least spent on food an amount of $261.01 per week on an average as suggested from the third quartile. The minimum weekly expenditure on food was found to be $44.31 and the maximum take home pay per week was $373.

Table 6

            The relationship between the weekly take home pay and the weekly expenditure on food is quantified using the correlation coefficient and the value of the correlation coefficient was found to be 0.899. The two variables thus have strong and positive linear relationship between each other.

Q5.

• The dependent variable or the response variable here is weekly food expenditure of a person and the independent variable is the weekly take home pay. The scenario seeks to establish a relationship between weekly food expenditure and the weekly take home pay. Naturally, the expenditure is dependent on the earnings that is a person would spend as per how much he earns in a week. The expenditure on food should also thus be influenced by the amount earned.
• The following scatter diagram depicts the relationship between the weekly expense on food by a person and his weekly take home pay, that is the amount of earnings he gets at hand per week. The plot shows the food expenditure against the take home pay and the scatter points are seen to have a linear relationship overall. The expenditure seems to increase as the take home pay increases and vice versa. The following chart shows the scatter plot, trend line, trend line equation and R²
• The trend line in the chart has a positive slope. The equation for the trend line as depicted on the chart is: y = 0.3133x + 40.859. The value of R² or the coefficient of correlation was also found to be 0.8094 that reflects strong positive correlation between the response and covariate. The following table gives the regression statistics for the linear regression line that was fitted to the data.

It is seen from the over regression significance measure given in the table below that the overall model that was fitted significantly explains the variation in the dependent variable, weekly food expenditure at 0.05 level of significance.

Table 7

            The following table gives the regression parameter estimates of the fitted regression model. It is seen that the covariate, weekly take home pay has a significant positive effect on the dependent variable, that is, food expenditure at 5% level of significance. The food expenditure per week increases as per 0.313 units with unit increase in week take home pay. The 95% of the confidence interval is between 0.288 and 0.337. This implies that the chance that the interval specified has a probability 0.95 of containing the value of the effect that weekly take home pay has on the weekly expenditure of food by a subject of the population on whom the study is being conducted. The estimate of the intercept was found to be 40.858. This means that if the weekly take home pay were zero then this is the amount that a person would expend on food per week.

Table 8

• The coefficient of determination, or R² statistic was found to be 0.809. This statistic gives the ratio between the variation explained by the regression model and the total variation. It is a measure of the goodness of fit of the model and indicates how well the model has been able to capture the variation in the response variable, which is about 80.94% in this case as suggested from the value of R squared value. The model thus captures a good portion of the variation.