A tele-marketing company wants to know if sales go up as they call more people per day but spend less time per call. The following is the data from nine randomly selected days. The information is the number of calls the salesperson makes in a day and the total amount of sales (in thousands of dollars).
Calls 25 29 33 37 43 48 52 55 67
Sales 3.7 4.2 4.2 5.0 4.7 5.3 4.9 5.6 5.9
e. Predict the amount of sales for the fourth observation in the data set.
f. Calculate the residual for that observation.
g. Construct the ANOVA table for this situation.
h. Calculate the coefficient of determination.
i. Interpret the coefficient of determination.
j. Using alpha = 0.05, use a model test to see if a linear relationship exists between the number of calls and sales.
k. A positive relationship is anticipated between these two variables. At alpha = 0.05, test to see if the evidence supports that anticipated sign.
l. Construct a 98% confidence interval for the population slope coefficient.
e. Fourth observation is 37 and sales for that is 4.53
f. Residual for that is 0.47
g. ANOVA table is
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 1282.38 | 1282.38 | 45.06913 | 0.000274 |
Residual | 7 | 199.1754 | 28.45363 | ||
Total | 8 | 1481.556 |
h. Co-efficient of determination is 86.56
i. 86.56 % calls are contributed to sales value
j. at 5% level of significance sales & calls are having linear relationship with P value of 0.00027.
K. A positive relationship is exist between them
L. 98 % of CI of Lower limit is 0.032 and Upper limit is 0.066
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