- Interpretation of Coefficients
Slope coefficient:
m = 13.0191
The above value indicates the rate of change
Intercept
c = 0.0328
At t =0, the above value would be observed
The value of sales (USD) for Federated Islands would be determined based on the given time.
For example, the sales for Federated Islands for a period of 8 years would be computed below:
Ln(Sales $) = 13.0191 + {0.0328 (Time)}
Time = 8
Ln(Sales $) = 13.0191 + {0.0328*8}
Sales = $587,428
Hence, the mean sales is $587,428
- Interpretation of coefficient of determination
R² = 0.8067
80.67% change in dependent variable explained
- Interpretation of correlation coefficient
R = 0.8982
High positive correlation between the variables
- Interpretation of standard error
S.E.= 0.1206
Average error stands at 0.1206
- Interpretation of 95% confidence interval for slope coefficient
Lower limit of 95% confidence interval = 0.0259
Upper limit of 95% confidence interval = 0.0397
There is 95% likelihood that the ln(sales) would increase by 0.0259 to 0.0397, when the time is increased by 1 unit
Hypothesis Testing
To check whether the slope coefficient is significant or not.
H? : β^1 = 0
H? : β^1 ≠ 0
- Level of significance = 5%
- Test statistics
t = slope coefficient / Standard error
t = 0.0328/0.0033 = 9.798
- The p value corresponding to slope coefficient.
P = 0.000
- It can be seen that the p value is lower than the level of significance and therefore, sufficient evidence present to reject the null hypothesis and to accept the alternative hypothesis.
Thus, the slope coefficient (time) is significant.![]()
Least Square Regression Line Equation
Ln(y) = mx+ c
Ln (Sales $) = 12.0094-(0.0125 *year) +(0.00*GDP) –(0.0281 *Price Index) + (0.00* Population)+ (0.0160* Survey Score) + (0.0605 * Advertisement) + (0.0399* Stores)
Intercept
- Interpretation of coefficient of determination
R² = 0.9947
99.47% variation in dependent variable jointly explained
- Interpretation of correlation coefficient
R = 0.9974
High positive correlation between variables
- Interpretation of standard error
S.E.= 0.0232
Average standard error stands at 0.0232
- Interpretation of adjusted R square
Adjusted R square = 0.9925
Comparable to R square implying that majority of the independent variables are significant
F test
H? : All slopes can be assumed as insignificant and hence zero
H? :Atleast one slope is significant and hence non-zero
ANOVA Table
Significance F or p value is 0 indicating rejection of H0 and hence linear regression model is significant
Hypothesis testing
H? : Slope coefficient is insignificant and hence zero
H? :Slope coefficient is significant and hence non-zero
Level of significance = 5%
From the above table, p values for all slope coefficients except population are less than 0.05 indicating that all independent variables except population are significant for estimating of sales
The mean regression coefficients for
The given independent variables lie
between.:
Years (-0.0187 to -0.0063)
GDP US$ (0.0000 to 0.0000)
Price Index (-0.0367 to -0.0195)
Population (0.0000 to 0.0000)
Survey Score (0.0053 to 0.0268)
Advertisement (0.0461 to 0.0747)
Stores (0.0212 to 0.0585)
