Simple Linear Regression Analysis for Sales and Survey per Capita Consumption

Assignment 6
Simple linear regression
Question (a)
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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f(x) = 2.65335495743383 x + 0.714391809620883
R² = 0.471453809032861
Scatter Plot of Sale and Survey per Capita Consumption
Sales Linear (Sales)
Survey per capita consumption
Sales
*The graph is a scatter plot indicating the relationship between sales and per capita consumption of
alcohol. The independent variable (predictor variable) is the survey’s per capital consumption of
alcohol, while the dependent variable is sales.
Question (b)
The graph indicates that there exists a linear relationship between the variables, sales and
per capita consumption of alcohol. The linear relationship has an upward slope indicating that the
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relationship between the two variables is positive. This means that an increase in the per capita
consumption will lead to an increase in the sales.
To understand the strength of the relationship, we look at the R-squared of the linear
equation of the graph below. R2 = 0.4715, meaning that 47.15% of the variation in sales can be
explained by changes in the per capita consumption of alcohol from the survey. Therefore, the
linear relationship between the two variables is moderately weak.
The graph also indicates some outliers in the survey data. These are data points that appear
to be unusually far away from the general pattern of the linear trendline. The outliers are seen to be
three data points where the sales are extremely high for the given per capital consumption.
Question (c)
The simple linear regression output for the data is given below:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6866
R Square 0.4715
Adjusted R Square 0.4604
Standard Error 0.3619
Observations 50
ANOVA
df SS MS F Significance F
Regression 1 5.6086 5.6086 42.8151 0.0000
Residual 48 6.2878 0.1310
Total 49 11.8964
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.7144 0.2587 2.7613 0.0081 0.1942 1.2346 0.1942 1.2346
Survey 2.6534 0.4055 6.5433 0.0000 1.8380 3.4687 1.8380 3.4687
Line of best fit:
Let x = Survey per capita consumption
Let y = Sales
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