a. Find the correlation coefficient: T= Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: = 0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate.
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.
![e. Interpret r2 :
O 83% of all customers will spend the average amount of money at the store.
O Given any group that spends a fixed amount of time at the store, 83% of all of those customers
will spend the predicted amount of money at the store.
There is a 83% chance that the regression line will be a good predictor for the amount of
money spent at the store based on the time spent at the store.
O There is a large variation in the amount of money that customers spend at the store, but if you
only look at customers who spend a fixed amount of time at the store, this variation on
average is reduced by 83%.
f. The equation of the linear regression line is:
I (Please show your answers to two decimal places)
g. Use the model to predict the amount of money spent by a customer who spends 14 minutes at the
store.
Dollars spent =
(Please round your ansvwer to the nearest whole number.)
h. Interpret the slope of the regression line in the context of the question:
O The slope has no practical meaning since you cannot predict what any individual customer will
spend.
For every additional minute customers spend at the store, they tend to spend on averge $3.64
more money at the store.
O As x goes up, y goes up.
i. Interpret the y-intercept in the context of the question:
The average amount of money spent is predicted to be $3.08.
Olf a customer spends no time at the store, then that customer will spend $3.08.
O The y-intercept has no practical meaning for this study.
O The best prediction for a customer who doesn't spend any time at the store is that the
customer will spend $3.08.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3d9db3-740f-497e-a2a5-fa4d7d0727de%2F03833b43-6e07-4581-9abd-75dba6708d1c%2Fampipth_processed.png&w=3840&q=75)
![A grocery store manager did a study to look at the relationship between the amount of time (in minutes)
customers spend in the store and the amount of money (in dollars) they spend. The results of the survey
are shown below.
Time
Money
30
13
21
10
13
17
27
103
63
99
29
50
51
103
a. Find the correlation coefficient: r=
Round to 2 decimal places.
b. The null and alternative hypotheses for correlation are:
Ho:
Hj: ?v + 0
= 0
The p-value is:
(Round to four decimal places)
c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context
of the study.
There is statistically insignificant evidence to conclude that a customer who spends more time
at the store will spend more money than a customer who spends less time at the store.
There is statistically significant evidence to conclude that there is a correlation between the
amount of time customers spend at the store and the amount of money that they spend at the
store. Thus, the regression line is useful.
O There is statistically significant evidenoce to conclude that a customer who spends more time at
the store will spend more money than a customer who spends less time at the store.
O There is statistically insignificant evidence to conclude that there is a correlation between the
amount of time customers spend at the store and the amount of money that they spend at the
store. Thus, the use of the regression line is not appropriate.
d. r=
(Round to two decimal places)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3d9db3-740f-497e-a2a5-fa4d7d0727de%2F03833b43-6e07-4581-9abd-75dba6708d1c%2Fozw9yen_processed.png&w=3840&q=75)
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