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STAT102 Business Data Analysis

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STAT102 Business Data Analysis

0 Download2 Pages / 442 Words

Course Code: STAT102
University: Australian Catholic University

MyAssignmentHelp.com is not sponsored or endorsed by this college or university

Country: Australia

Question:

a)Is there a correlation between rainfall and average yield to suggest a linear relationship?  Please explain the correlation, if it exists.
b)Draw a scatter plot and the least square line.
c)Is the least square line a good fit for the data?  Please explain.
d)Re-draw the scatter plot and the least square line without Year 5 data.
e)Is the least square line in d) a good fit for the data?  Please explain.
f)Please suggest a plausible reason why Year 5 had the highest rainfall and yet the lowest average yield.

Answer:

Question 1

Below is a chart line indicating the trend of private capital expenditure during 12 quarters. Capital expenditure (in millions) appear on the Y-axis while the quarters appear on the X-axis.

Figure 1

A secular trend provides a general tendency of time series data for a sustained period of time (Wooldridge, 2015). From secular trend for our data draws a zigzag pattern characterized by a continuous increase and decrease on private expenditure. The overall effect of the rise and decline is stability at around 27,000 million.
The chart displays a seasonal trend. The chart contains periodic peaks and lows implying that      private capital expenditure is high during some period of the year and low during other seasons.
The expenditure at period Quarter 13 is likely to be 35,000 million. Extrapolating the graph, it is evident that, expenditure is still rising towards point 35,000 million then it would decline in response to the season.

Question 2

There is no linear relationship between average yield and rainfall. The correlation between the 2 variables is 0.226. However, the significance level (0.667) is greater than 0.05 implying that there exist no linear correlation between average yield and rainfall.

Test of correlations

 

 

Rainfall

avarageyield

Rainfall

Pearson Correlation

1

.226

Sig. (2-tailed)

 

.667

N

6

6

Table 1
(b) Below is a scatter plot and least squares line showing relationship between average yield and rainfall
Figure 2
(c) The least squares squares line is not good fit for the data. Most of the values are located outside the line. Year 5 data  can be regarded as outliers
(d) Figure 3 below shows a scatter plot of rainfall and average yield when year 5 data is removed.
Figure 3
(e) The scatter plot above is a good fit for the data. All data points are located within the line. The explanation is also supported by table 2 below which indicates that the correlation coefficient of rainfall and avarageyield is 0.99 with a p value of 0.000 which is less than the level of significance. When P-value is less than level of significance, it implies that there is significant correlation between the variables (Chatfield, 2018).

Correlations

 

 

Rainfall

avarageyield

Rainfall

Pearson Correlation

1

.999**

Sig. (2-tailed)

 

.000

N

5

5

avarageyield

Pearson Correlation

.999**

1

Sig. (2-tailed)

.000

 

N

5

5

**. Correlation is significant at the 0.01 level (2-tailed).

Table 2
(f) Normally, the higher the rainfall, the higher the average yield. However, when rainfall goes beyond a certain amount, production (yield) might decline. Some crops require moderate amounts of rainfall to produce optimally. A rise in rainfall above a certain range might promote crop diseases, erosion, or flooding which has negative impact on yields
References
Chatfield, C. (2018) Introduction to multivariate analysis. Abingdon: Routledge.
Wooldridge, J.M. (2015) Introductory econometrics: A modern approach. Ontario: Nelson Education.

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