In order to determine a realistic price for a new product that a company wants to market the company’s research department selected 10 sites thought to have essentially identical sales potential and offered the product in each at a different price. The resulting sales are recorded in the accompanying table: PRICE ($) SALES ($1,000's) 15.00 15 15.50 14 16.00 16 16.50 9 17.00 12 17.50 10 18.00 8 18.50 9 19.00 6 19.50 5 a) Explain carefully, which of the variables above is the independent variable and which is the dependent variable. b) Draw a scattergram of the above data. Does it seem that the two variables are somewhat related? If yes, how do they seem to be related? c) Find the equation of the sample regression line. d) Interpret the meaning of the coefficients of the equation of the sample regression line. e) At 5% level of significance, is there evidence of a linear relationship between the sales and price? f) At 5% level of significance, can we conclude that sales are negatively impacted as the price increases? g) How useful is the linear model you have established in this problem. Assess the model and explain carefully the procedures used in the assessment. h) Estimate the slope of the actual equation of the regression line using a 95% confidence interval and interpret this interval.
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.
In order to determine a realistic price for a new product that a company wants to market the company’s research department selected 10 sites thought to have essentially identical sales potential and offered the product in each at a different price. The resulting sales are recorded in the accompanying table:
| PRICE ($) | SALES ($1,000's) |
| 15.00 | 15 |
| 15.50 | 14 |
| 16.00 | 16 |
| 16.50 | 9 |
| 17.00 | 12 |
| 17.50 | 10 |
| 18.00 | 8 |
| 18.50 | 9 |
| 19.00 | 6 |
| 19.50 | 5 |
a) Explain carefully, which of the variables above is the independent variable and which is the dependent variable.
b) Draw a scattergram of the above data. Does it seem that the two variables are somewhat related? If yes, how do they seem to be related?
c) Find the equation of the sample regression line.
d) Interpret the meaning of the coefficients of the equation of the sample regression line.
e) At 5% level of significance, is there evidence of a linear relationship between the sales and price?
f) At 5% level of significance, can we conclude that sales are negatively impacted as the price increases?
g) How useful is the linear model you have established in this problem. Assess the model and explain carefully the procedures used in the assessment.
h) Estimate the slope of the actual equation of the regression line using a 95% confidence interval and interpret this interval.
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