The data provided here represent the number o radio & TV ads (in 1000) used and the sales in thousand dollars for a concert. (a) Create a scatterplot of these data using sales for vertical axis. Move and resize it so that it appears between columns D and H below this question.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![### Linear Relationship between Advertising and Sales
#### Dataset
The table below presents the data for the number of radio & TV ads (in 1000s) utilized for a concert and the corresponding sales figures (in $1000).
| Radio & TV ads (in 1000s) | Sales ($1000) |
|----------------------------|---------------|
| 0 | 1119 |
| 0 | 973 |
| 25 | 875 |
| 25 | 625 |
| 30 | 910 |
| 30 | 971 |
| 35 | 931 |
| 35 | 1177 |
| 40 | 882 |
| 40 | 982 |
| 45 | 1628 |
| 45 | 1577 |
| 50 | 1044 |
| 50 | 914 |
| 55 | 1329 |
| 55 | 1330 |
| 60 | 1405 |
| 60 | 1436 |
| 65 | 1521 |
| 65 | 1741 |
| 70 | 1866 |
| 70 | 1717 |
#### Instructions
**(a)** Create a scatterplot of these data using sales for the vertical axis. Move and resize it so that it appears between columns D and H below this question.
![Insert scatterplot here]
**(b)** Compute the correlation between the number of ads and sales. Provide your final answer in the yellow highlighted cell.
**Answer:**
\[ \text{Correlation: } \]
\[ CELL D27 \]
**(c)** Perform a simple linear regression analysis using sales as the response variable (y). Provide your answer starting at the yellow highlighted cell.
**Answer:**
\[ \text{Linear Regression Analysis:} \]
\[ CELL D34 \]
This setup helps in understanding the relationship between the ads and the sales numbers. The scatterplot will visually display this relationship, while the correlation will quantify the strength and direction of the relationship. The linear regression analysis will provide insights into how much sales are expected to change with a change in the number of ads.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bf6b58d-ef43-404d-8e44-e8a8dab82f8c%2F9832f87b-e762-4b97-b096-4cfcff760dcb%2Fqnapj2a.jpeg&w=3840&q=75)
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