The cost of a leading liquid laundry detergent in different sizes is given below. Size (ounces) Cost ($) Cost per ounce 16 3.19 32 4.39 64 5.59 200 10.99 Part (a) Using "size" as the independent variable and "cost" as the dependent variable, make a scatter plot. Part (b) Does it appear from inspection that there is a relationship between the variables? Why or why not? Yes, it appears that cost increases with size. No, there is no visible relationship between the variables. Part (c) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) ŷ = + x
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
| Size (ounces) | Cost ($) | Cost per ounce |
|---|---|---|
| 16 | 3.19 | |
| 32 | 4.39 | |
| 64 | 5.59 | |
| 200 | 10.99 |
-
Part (a)
Using "size" as the independent variable and "cost" as the dependent variable, make a scatter plot.
Part (b)
- Yes, it appears that cost increases with size.
- No, there is no visible relationship between the variables.
-
Part (c)
Calculate the least squares line. Put the equation in the form of:ŷ = a + bx.(Round your answers to three decimal places.)
ŷ = + x -
Part (d)
Find thecorrelation coefficient r. (Round your answer to four decimal places.)
r =
Is it significant?Yes or No ? -
Part (e)
If the laundry detergent were sold in a 40-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)
$ -
Part (f)
If the laundry detergent were sold in an 82-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)
$ -
Part (g)
Use the two points in parts (e) and (f) to plot the least squares line. Show the points
Part (h)
- A line is the best way to fit the data because there seems to be a relationship between the variables.
- A line is not the best way to fit the data because when you purchase double the amount of detergent, the cost does not double.
- A line is the best way to fit the data because the data follow an almost perfect positive linear trend.
- A line is not the best way to fit the data because it should touch each data value in the
scatter diagram .
Part (i)
- Yes, (16, 3.19) is an outlier.
- Yes, (200, 10.99) is an outlier.
- Yes, (16, 3.19) and (200, 10.99) are outliers.
- No, there are no outliers.
Part (j)
- The least squares line is valid for predicting what a 300-ounce container of laundry detergent would cost because all equations can be used to make predictions.
- The least squares line is valid for predicting the cost of a 300-ounce container of detergent because it is possible to purchase 300 ounces.
- The least squares line is not valid for predicting the cost of a 300-ounce container of detergent because 300 ounces is beyond the
range of x-values. - The least squares line is not valid for predicting the cost of a 300-ounce container of detergent because the cost would be unreasonable.
Part (k)
Interpret the slope.Select the following
- As the cost of liquid laundry detergent increases by $1, the detergent size increases by this many ounces.
- As the number of ounces increases by one, the cost of the liquid laundry detergent increases by this many dollars.
Since you have posted a question with multiple sub parts, we will solve first 3 sub parts for you. To get remaining sub parts solved, please repost the complete question and mention the sub parts to be solved.
Let X be the size as independent variable and
Y be the cost as dependent variable
n= number of observations = 4
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