Capacity (in TB) Price (in $) 0.080 29.95 0.120 35.00 0.250 49.95 0.320 69.95 1.0 99.00 2.0 205.00 4.0 449.00
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.
Disk drives again In Chapter 6, Exercise 4, we saw some
data on hard drives. After correcting for an outlier, these
data look like this: we want to predict Price from Capacity.
Variable Coefficient
Intercept 8.1006
Num_Workers 0.9134
Dependent variable is Sales
R-squared = 93.2,
s = 1.477
R-squared = 98.8,
s = 17.95
Variable Coefficient
Intercept 18.617
Capacity 103.929a) Write the regression equation. Define the variables
used in your equation.
b) What does the slope mean in this context?
c) What does the y-intercept mean in this context? Is it
meaningful?
d) What would you predict for the price of a 3.0 TB drive?
e) You found a 3.0 TB drive for $300. Is this a good buy?
How much would you save compared to what you
expected to buy?
f) Does the model overestimate or underestimate the
price for a 3.0 TB drive?
note :
Since you have posted multiple questions with multiple sub parts, we will provide the solution only to the first three sub parts of the first question as per Q&A guidelines. Please repost the remaining question by specifying the sub parts need to be answered.
As per the question we are given the result of a regression analysis that was conducted to study the relationship between Price and Capacity. The analysis found that there are two regression equations: one for predicting Sales and one for predicting Price. The regression equation for predicting Sales has an R-squared value of 93.2, which means that 93.2% of the variance in Sales can be explained by the independent variable Num_Workers. The regression equation for predicting Price has an R-squared value of 98.8, which means that 98.8% of the variance in Price can be explained by the independent variable Capacity. The slope and y-intercept values for both regression equations are also provided.
Now we have to :
- Write the regression equation. Define the variables used in your equation.
- Explain the meaning of slope in this context.
- The meaning of the y-intercept in this context.
From the information provided, it appears that there are two regression equations: one for predicting Sales and one for predicting Price.
For the regression equation for predicting Sales, the dependent variable is Sales, and the independent variables are the intercept and Num_Workers. The equation can be written as:
Sales = 8.1006 + 0.9134 * Num_Workers
In this equation, Sales is the dependent variable, which is the variable that we are trying to predict. Num_Workers is the independent variable, which is the variable that we are using to predict Sales. The coefficient of Num_Workers is 0.9134, which means that for every unit increase in Num_Workers, we expect to see a 0.9134 unit increase in Sales. The intercept is 8.1006, which is the value of Sales when Num_Workers is zero.
For the regression equation for predicting Price, the dependent variable is Price, and the independent variable is Capacity. The equation can be written as:
Price = 18.617 + 103.929 * Capacity
In this equation, Price is the dependent variable, which is the variable that we are trying to predict. Capacity is the independent variable, which is the variable that we are using to predict Price. The coefficient of Capacity is 103.929, which means that for every unit increase in Capacity, we expect to see a 103.929 unit increase in Price. The intercept is 18.617, which is the value of Price when Capacity is zero.
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