ONA model is developed for forecasting of sale and the effects of three independent variables , advertising expenditure (X1), Price (X2), and time (X3) resulted in the following. Regression Statistics Standard Error 232.29 Table 1: ANOVA df SS MS F Regression 3 53184931.86 ? ? Residual ? 1133108.30 ? Total 24 54318040.16 Table 2: regression Coefficients Standard Error t Stat Intercept 927.23 1229.86 ? Advertising (X1) 1.02 3.09 ? Price (X2) 15.61 5.62 ? Time (X3) 170.53 28.18 ? d. At 95% confidence, determine whether or not the over all regression model is significant. Fully explain how you arrived at your conclusion (give numerical reasoning) and what your answer indicates. e. At 95% confidence determine which variables are significant and which are not. Explain how you arrived at your conclusion (Give numerical reasoning). f. Compute the confidence interval for the regression coefficient of independent variable Advertising (let ᾳ=5%) g. Given the confidence interval for the regression coefficient of independent variable Advertising computed in question (f) , Is the coefficient significant or not? Justify your answer
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Problem I
ONA model is developed for forecasting of sale and the effects of three independent variables , advertising expenditure (X1), Price (X2), and time (X3) resulted in the following.
|
Regression Statistics |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Standard Error |
232.29 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Table 1: ANOVA |
|
|
|
|
|
|
|
df |
SS |
MS |
F |
|
|
Regression |
3 |
53184931.86 |
? |
? |
|
|
Residual |
? |
1133108.30 |
? |
|
|
|
Total |
24 |
54318040.16 |
|
|
|
|
Table 2: regression
|
|
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
|
|
|
Intercept |
927.23 |
1229.86 |
? |
|
|
|
Advertising (X1) |
1.02 |
3.09 |
? |
|
|
|
Price (X2) |
15.61 |
5.62 |
? |
|
|
|
Time (X3) |
170.53 |
28.18 |
? |
|
|
|
d. |
At 95% confidence, determine whether or not the over all regression model is significant. Fully explain how you arrived at your conclusion (give numerical reasoning) and what your answer indicates. |
|
e. |
At 95% confidence determine which variables are significant and which are not. Explain how you arrived at your conclusion (Give numerical reasoning). f. Compute the confidence interval for the regression coefficient of independent variable Advertising (let ᾳ=5%) g. Given the confidence interval for the regression coefficient of independent variable Advertising computed in question (f) , Is the coefficient significant or not? Justify your answer |
Step by step
Solved in 6 steps
