Question

Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following. The week 6 spreadsheet can be helpful in this work.

1. Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret.

2 Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.

3 Determine the correlation coefficient. Interpret.

4 Determine the coefficient of determination. Interpret.

5 Test the utility of this regression model by completing a hypothesis test of b=0 using α=0.10. Interpret results, including the p-value.

6 Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.

7 Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.

8 Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.

9 Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.

10 What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.

11 Describe a business decision that could be made based on the results of this analysis. In other words, how might the business operations change based on these statistical results. .

Sales (Y) Calls (X1) Time (X2) Years (X3) Type

40 144 17.4 0.00 NONE

46 145 16.8 0.00 ONLINE

37 152 19.8 0.00 NONE

47 164 15.3 0.00 ONLINE

42 135 16.1 0.00 NONE

44 169 8.9 0.00 ONLINE

52 173 18.6 0.00 ONLINE

53 184 15.2 0.00 ONLINE

49 152 22.3 0.00 ONLINE

49 166 16.2 0.00 ONLINE

45 185 13.3 1.00 ONLINE

47 157 14.3 1.00 GROUP

42 148 16.9 1.00 NONE

43 131 18.5 1.00 NONE

44 150 18.4 1.00 NONE

43 148 15.9 1.00 ONLINE

55 189 12 1.00 ONLINE

49 188 20.4 1.00 NONE

51 190 11.3 1.00 ONLINE

37 137 18.1 1.00 ONLINE

51 167 16.2 1.00 ONLINE

37 130 15.6 1.00 GROUP

37 142 18.5 1.00 NONE

46 153 14.1 1.00 ONLINE

39 149 18.8 1.00 GROUP

46 151 16 1.00 GROUP

45 158 13.9 1.00 ONLINE

46 172 12.5 1.00 ONLINE

47 188 16.3 1.00 NONE

37 148 16.2 1.00 GROUP

46 162 12.1 1.00 GROUP

52 177 14.5 1.00 ONLINE

48 175 13.7 1.00 ONLINE

40 150 10.8 1.00 GROUP

53 182 10.5 1.00 ONLINE

54 197 11.8 1.00 ONLINE

46 148 13.1 1.00 GROUP

41 153 14.7 1.00 GROUP

44 169 13.6 1.00 ONLINE

47 176 14.1 2.00 ONLINE

47 183 12.8 2.00 ONLINE

48 136 14.1 2.00 ONLINE

52 197 13.9 2.00 ONLINE

37 120 12 2.00 NONE

49 184 16.7 2.00 ONLINE

43 173 19.8 2.00 ONLINE

42 153 15.5 2.00 GROUP

37 133 19.8 2.00 NONE

42 154 14.8 2.00 ONLINE

53 178 13.2 2.00 ONLINE

45 138 18.9 2.00 NONE

42 167 18 2.00 NONE

48 171 13 2.00 GROUP

46 162 16.2 2.00 ONLINE

49 149 21.1 2.00 GROUP

48 174 18.6 2.00 GROUP

45 173 17.6 2.00 ONLINE

45 155 18.9 2.00 GROUP

44 159 18.1 2.00 ONLINE

54 174 10.8 2.00 NONE

44 139 15.2 2.00 NONE

41 158 19.3 2.00 ONLINE

43 145 18.6 2.00 NONE

47 193 13.5 2.00 ONLINE

38 145 17.1 2.00 NONE

50 184 15.6 2.00 ONLINE

41 128 15.5 2.00 NONE

45 177 14.2 2.00 GROUP

49 170 16.1 3.00 NONE

38 122 19.3 3.00 GROUP

46 171 13.6 3.00 GROUP

37 148 15.7 3.00 GROUP

42 167 17.7 3.00 ONLINE

44 148 13.5 3.00 GROUP

45 164 16.7 3.00 NONE

45 146 12 3.00 GROUP

48 177 13.9 3.00 ONLINE

49 160 13.6 3.00 GROUP

46 149 17.8 3.00 NONE

45 140 11 3.00 GROUP

45 130 20.6 3.00 GROUP

43 166 17.6 3.00 ONLINE

44 188 12.9 3.00 GROUP

41 157 11.5 3.00 ONLINE

41 155 13.6 3.00 GROUP

43 153 15.2 3.00 GROUP

37 145 18 3.00 NONE

34 133 15.2 4.00 GROUP

51 177 11.4 4.00 NONE

43 169 13.3 4.00 NONE

39 156 13.3 4.00 NONE

40 125 12.2 5.00 NONE

44 182 15.5 5.00 NONE

48 156 15.1 4.00 ONLINE

43 148 14.5 4.00 ONLINE

39 138 17.7 4.00 GROUP

42 160 10.6 4.00 NONE

54 180 11.8 5.00 GROUP

51 167 12.6 6.00 ONLINE

48 165 19.8 6.00 ONLINE

and i need question 5 to 11 answer for it thank you

Answer 1

Dependent variable: sales (Y)

Independent variable: Calls (X1)

1 to 4

The regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Sales' column, Input X Range: 'Calls' column, Confidence Level = 99%, and tick box for LINE FIt Plot then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

1)

The scatter plot with the trend line (Line Fit Plot)

From the plot, we can see that there is a positive linear trend between the sales and calls

2)

From the regression output summary,

The regression equation is,

3)

From the regression output summary,

The correlation coefficient value is,

Multiple R

0.6932

Interpretation: There is a moderate positive linear correlation between the dependent variable sales and independent variable calls.

4)

From the regression output summary,

The coefficient of determination (R square) value is,

R Square

0.4805

Interpretation: The R-square value tells, how well the regression model fits the data values. The R-square value of the model is 0.4805 which means, the model explains approximately 48.05% of the variance of the data value.

5)

Hypothesis

Null Hypothesis:

Alternate Hypothesis:

The P-value is obtained in regression analysis,

	P-value		Significance level	Decision
Calls	1.3252E-15	<	0.05	The null hypothesis is rejected,

Conclusion: The P-value for the independent variable is less than 0.05 at a 5% significance level hence we can conclude that independent variable is statistically significant in the model.

6)

Since the model is statistically significant compared to the intercept only model and the independent variable significantly fit the model. The R square value is approximately 0.5 which means there is moderate effect size.

Based on this evidence we can say that the ability of the independent variable to predict the dependent variable is moderate.

7)

From the regression output summary, the 95% confidence level for the slope coefficient is,

Interpretation: Since the confidence interval doesn't include zero, the estimation of the coefficient is statistically significant at a 5% significance level.

8)

let X = 150,

The dependent variable value is,

Now, the confidence interval for Xpredictor = 150 is obtained using the formula,

From the data values,

From the regression output summary,

The standard error of the regression is,

Standard Error

3.4289

The t-critical value is obtained from t-distribution table for significance level = 0.01 and degree of freedom = n - 2 = 98

now,

9)

The 99% prediction interval for the dependent variable is obtained using the following formula,