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Answer all the following questions:
Please answer the following questions:
The R2=0.762 in the final regression model, while in the first regression model, R2=0.581 showing that the last regression model is better and the data fits the model well than the first model. 76.2% of the variation in the dependent variable, annual sales can be explained by the independent variables, the number of customers, and monthly income. This is a statistically significant percentage.
The ANOVA table shows a significant linear relationship between annual sales and the independent variables: number of customers and monthly income, F(2,17) =580.655, p =.001. The p-value is less than alpha=0.05, and therefore we reject the null hypothesis.
Annual sales=42.635+ 15.182(number of customers) +7.027(monthly income)
Annual sales and number of customers have a statistically significant linear relationship, B=15.182,t stat=3.025, p=.005. An increase in the number of customers results in a corresponding increase in annual sales. Annual sales and monthly income have a statistically significant linear relationship, B=7.027,t stat=2.786, p=.008. Growth in the monthly income results in a corresponding increase in the annual sales, and vice versa.
| N | Variance | Range | Mean | Std. Deviation | |
| Sample data
Valid N (listwise) |
18
18 |
42.499 | 28.00 | 168.50 | 6.519 |
Please answer the following questions (Note: calculation steps are required in the answers for each of following questions):
(a.1) set up a 95% confidence interval estimate to the average strength of the stored cardigans. (5%)
CI= 100(1-)%, therefore 30.1162
Z=Z=Z0.025=1.96
X⁻- Z<< X⁻+ Z
168.50-1.96<< 168.50+1.96
95% CI=165.488<<171.511
(a.2) what sample size is required if the Margin of Error is 1 at 95% of confidence for the estimate of the average strength of the stored cardigans? (5%)
E= Z
E=1
1= 1.96
n=(1.96*6.519)2
n=163.2578
=Approximately 163
n standard deviation of 6 kPa, answer the following wing questions:
(b.1) 60% of the stored cardigans will have strength between what two values of kPn (the two values are syininetricall y distributed around the mean)? (5%)
P(m<X<n)=0.6
or, P(X<n)-P(X<m)=0.6
P(Z<z)-P(Z<-z)=0.6
Z=,,,,-Z=
2P(Z<z)-1=0.6
P(Z<z)=0.8
From normal table: Z=0.8416
0.8416=
n=173.0197
-0.8416=
m=162.9503
Then the two values between which strength of the 60% stored cardigans will lie are 173 kPa and 163 kPa.
(b.2) what percent of the stored cardigans will have strength either below 1 56 kPa or larger than 180 k Pa (5%)
P(X>180 or X<156)
=P(X>180)+P(X<156)= P(Z>2)+P(X<-2)
=1- P(Z>2)+1- P(Z<2)=2{ 1-P(Z<2)}
P(Z<2)=0.97724
=2 (1-0.97724)=0.0455
=0.0455*100=4.55%
After entering the data into SPSS, the variables displayed will be satisfactory level which is the independent variable, and the three schools, A, B, and C, that is the dependent variable. The next step is to ensure that the dependent variable should be continuous and the independent variable is categorical. The satisfactory level is a Likert scale and is treated as a continuous variable. The schools are categorical: school A, school B, and school C.Click Analyze—Compare means—One-way ANOVA. Under the one-way ANOVA, the school categories is inputted under the factor box and the satisfactory level under the dependent variable box. Click on the Post_Hoc button, then select Tukey. Click on the continue button then the options button. Under options, click descriptives the select continue, then finally the ok button to run the analysis. The results are then interpreted and the statistical significance of the satisfactory level of the three groups related.
(Word limit: Maximum 120 words for each of following questions) (48%)
Both methods of data grouping do not create a distinction between dependent and independent variables. However, the two are different in that factor analysis decreases the number of variables by putting them in small factors. In contrast, cluster analysis reduces observations’ numbers by putting them in groups of small clusters. In simple terms, cluster analysis is a form of categorizing variables, while factor analysis simplifies observations.
The p-value method is the easiest method that computes a single value, the p-value, which is the significance level. The technique relates the p-value and the alpha, which is usually equal to 0.05. On the other hand, the manual method entails computing the test statistic and the critical value. This is tedious because it involves the computation of two factors. Conclusions are then made based on the given level of significance, usually 0.05.
Hierarchical clustering is always in the form of a tree. The trees usually entail a set of nested clusters. It works on structures that are not hyperspherical. On the other hand, K means the algorithm works best on hyperspherical groups such as spheres.
Correlation uses r to show the strength and direction of the association between variables. In contrast, regression uses beta coefficients to show the strength, direction, and cause and effect between variables. Correlations can only be carried out on two continuous variables, while in regression relationship of one dependent variable and multiple independent variables can be determined.
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