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The test which is used in the analysis of data is ANOVA test.
The p value in the ANOVA table shows 0.000 for all the four models. This tells that the differences between the means are statistically significant. This can be said by comparing the value with the significance level of 5 per cent to assess the null hypothesis.
The model summary shows the r squared. The r squared shows the goodness of fit of the model. For all the four models, the r squared is high and greater than 0.7. This means that the variation in the dependent variable is highly explained by the independent variables. Also, a significant F means that the prediction is getting better as the variables are added in the next steps.
The coefficient table shows the value of slope coefficient and constant in the regression for all the four models. The significance value tells that the slope is statistically significant. The correlation is explained by the value of variance inflation factor. The value of 1 shows, there is no correlation. The value of 1 to 5 shows that there is moderate correlation and the value of more than 5 shows high correlation.
In this question, value of sales is regressed on the distance from nearest competitor. The model summary shows that the r squared of the regression is 0.58. This is a good fit. It shows that 58 percent of the change in the value of sales is explained by the distance of the nearest competitor.
The normality assumption is checked by comparing the histogram of a sample data and normal probability curve. The assumption states that the data should fit the bell curve shape before using any statistical tests. The histogram show that the data is slightly skewed. Also, the sample size is 14, which is very small. It becomes difficult to test the normality if the sample is small.
The ANOVA test shows the F value which is high. The large F ratio would mean that the variation among group means is greater than what is expected to see by chance. The coefficient table shows the value of coefficient of distance of the nearest competitor. The t value and the significance level tells us that the slope is highly statistically significant and there is positive impact of increase in distance on the value of sales.
The scatter plot shows that there is positive relationship between floor area and value of monthly sales. This can be seen as the floor length is between 1000 to 2000, the value of sales is between 2000 to 4000. When the floor length is increased and is between 2000 to 3000, the value of sales increases and is between 4000 to 8000. At higher values of floor length that is greater than 5000, the value of sales also rises to levels more than 8000. For checking the normality assumption, the sample size should be large. In this case, the sample size is 14, which is very small. Thus, it becomes difficult to see if the sample is small.
The correlation table shows that the Pearson correlation coefficient between floor area and value of monthly sales is 0.954, which is very high and close to 1. The t value is 0.00 which is less than 0.01. The t test shows that correlation is highly significant at 0.01 level. This means that there is statistical positive relationship between floor area and value of sales.
The dependent variable, gallons per 100 miles are regressed on four independent variables. The model summary table shows the r squared and adjusted r squared. The both measures of goodness of fit is more that 0.8, which is quite high. This tells us that the data is very accurately fit. The change in the dependent variable is mostly explained by the four independent variables that are included. The ANOVA test shows the mean square and the F value. We can see that the significance value is 0.000, which is below 0.05 and, therefore, it is statistically significant. The model very well fits the data.
The coefficient table shows the value of coefficient of all the four independent variables. The t value and the significance value shows that all the coefficients are statistically significant at 0.01 level except the seconds to reach to speed 60 to 0, which is significant at 0.05 level.
The histogram shows that the data is normally distributed and is not skewed. The scatterplot shows that there is no relationship between the standardised residual and the predicted value.
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