In defining a hypothesis for the study, the researcher of the study took into consideration the variables to form a predication in the mind of the affected changes likely to occur if the independent variables are varied across the scale. The multiple regression is used to find the future value amount of the sales when provided with data concerning the adverts, radio plans, and airplay image budgets. The three variables mentioned above affect the direction of sales for the firm. The reason is that they have a direct relationship, which can be equated to linearity. By combining the diverse linear regression models in the case study resulted in a multiple regression model, which was used in the determination of the budgeted sales in the firm. The following is a simple illustration of linear regression analysis:
Y=Mx+C.
Y represents the sales in values
M is the constant which is applied in the determination of the future values for the sales and constant amounts represented by C; thus, fixed, variable costs. The above regression utilizes the idea of two known variables. There is the case where the independent variables are more than two, such as the case presented. The following is an example of the regression model applicable to knowing whether the hypothesis can be rejected or accepted. In most cases, the hypothesis is stated as a null hypothesis. If one accepts or rejects the null hypothesis, then the multiple regression acts as a predictive tool for knowing variable quantities once the due process has taken its course. The general regression for the case is as follows:
Y = C + X1+ X2 + X3
Where;
Y = sales
X1 = adverts
X2 = radio plans
X3 = airplay/ brand images
C- Constant
The hypothesis utilized in the study is the null hypothesis, and they are stated as below:
Null hypothesis
H01: The various adverts placed in the print and social media do not have a major effect on the number of sales realized by the enterprise.
H01: The radio plans instituted by the firm did not have a significant impact on the sales revenue generated for the year.
H01: The branding of the different images of company products and services had a little or no impact on the number of sales for that period.
Outlining the hypothesis
Apparently, the figures obtained for the t-test indicated a p-value of 0.00, which prompted the rejection of the null hypothesis. The value is acceptable at a significant level of 0.05. This means that radio plans, branding, and adverts have a primary impact on company sales for a specific time. The reason is that the three marketing techniques tend to provide the clients with broader network coverage of educating them of the different services and commodities manufactured by the organization. The direct relationship established by the variables creates an element of linearity and collinearity, which forms one of the assumptions of multiple regression models to hold. The three hypotheses support the fact that multiple regression was the best appropriate method of predicting future trends of the market to inform management of whether profit will increase or not to the following years or months.
Independent and dependent variable measurements
Sales –Dependent variable
Air play Images, advert and radio plans forms part of the independent variables.
Sales is not a constant figure and is measured by the amount of profit the firms make for the financial years. The sales can be in terms of quantifiable volumes or measured in ratios such as the return of the various items of the balance sheet or at the rate of which the stock is moving. Any changes in the form of the advert to place to the public has the significant effect of bringing massive changes into the organization sales. The reason is that these independent figures are not affected by other factors in the market as they privately institute forces on the sales variable.
Assessment of outliers
In the determination of the best line of fit, some variables may become outliers because they do not fit on the straight-line fit. For the purpose of using linear regression, coordinates were plotted on the Cartesian plane to get the liner line for the research. The outliers are mostly few in a scenario where the IV and DV are plotted on the graph. Most of the variables plotted, except for the incident of a number of plays on, forms a pattern that is not clearly reflected in the value output result. The assessment of outliers on the study involves two points which were probed further for clarification purposes.
Assumptions of multiple regression
The first postulate of the regression is that all the extra points will have a regular distribution pattern. This means that a linear expression model or line will be formed once the points are plotted onto the graph. Secondly, in the case of multiple regression, the issue of multicollinearity should not exist because the results would not be accurate in that case. The IV variables should not have a high correlation with one another as expressed on the table results of the case study. Thirdly assumption is that the error term of all the IV is the same across all the levels. In testing for error term similarity, a graph could be used where the residuals which had a specific standard are plotted against the discrete values (Field, 2017).
Tests for addressing the assumption
In most times, the multicollinearity, the correlation matrix is used in testing whether the IV is more or less correlated. The following is an example of the test explained above:
Variables Sales Adverts Airplay images Branding images

Sales 1.000

Adverts 0.328 1.000
0.000

Airplay images 0.826 0.623 1.0
0.002 0.002

Branding images 0.2433 0.346 0.656 1.0
0.000 0.508 0.838

From the table analysis, the R-value is 0.32 while the p-value is zero. On the case of adverts and sales, this means that the two variables are positively associated with one another; thus forming a linear regression model. The same argument applies to the airplay images and branding images because the p-values are all less than the recommended value of 0.005.
Examination and results of the assumption
The reason for the existence and application of the premises into the case study presented in the text is because there might arise due to instances of the variability of results, which cannot be relied upon to make decisions such planning and allocating resources to the various departments of the company. The results indicated that all the three IV had a high impact on the sales be in it quantities sold or amount received equivalent to the inventories sold.
Results interpretation
Conclusively, the analysis was based on the single t-test, where all the null hypothesis were rejected; thus showing that IV such as adverts do affect sales. The other focus was on the standard deviation where the less value, the more riskier the business was operating.
Reference
Field, A. (2017). Discovering statistics using IBM SPSS statistics: North American edition. NY: Sage publications.

QUESTION
Read the following case study and reply to the questions. Provide at least one scholarly reference.

Audiotech Electronics, founded in 1959 by a father and son, currently operates a 35,000-square-foot factory with 75 employees. The company produces control consoles for television and radio stations and recording studios. It is involved in every facet of production—designing the systems, installing the circuits in its computer boards, and even manufacturing and painting the metal cases housing the consoles. The company’s products are used by all the major broadcast and cable networks. The firm’s newest products allow television correspondents to simultaneously hear and communicate with their counterparts in different geographic locations. Audiotech has been very successful meeting its customers’ needs efficiently.

Audiotech sales have historically been strong in the United States, but recently, growth is stagnating. Even though Audio-tech is a small, family-owned firm, it believes it should evaluate and consider global expansion.

1. What are the key issues that need to be considered in determining global expansion?
2. What are some of the unique problems that a small business might face in global expansion that larger firms would not? Should Audiotech consider a joint venture?
3. Should it hire a sales force of people native to the countries it enters?