Question

uestion (2) (30 Marks A supermarket wishes to assess the effect of shelf display space on the sales of a product. The manager has tried out different shelf lengths for a week each and has recorded the resulting sales Sales (Es) Shelf length (metres) 155 173 85 228 186 148 130 156 178 107 120 110 0.8 1.2 0.5 1.8 1.4 0.9 1.1 1.3 1.6 0.7 0.9 1.0 Answer the following Questions (1) Plot the scatter diagram.(2 Marks) (2) Calculate the correlation coefficient and explain what it shows. (4 Marks) (3) Calculate the coefficient of determination and explain what it shows. (4 Marks) (4) Find the equation of the regression line. Interpret the coefficients of this equation. (5 Marks) (5) Plot the regression line on the scatter diagram. (2 Marks) (6) Forecast the sales for a shelf length of 0.6, 1.0 and 2.0 metres respectively. (2 Marks) (7) Write a report on your findings. (5 Marks) (8) Which hypotheses are used in testing the significance of the correlation coefficient? Which statistic is used? How many degrees of freedom are used (2 Marks) (9) Which hypotheses are used in testing the significance of the regression coefficient? (2 Marks) (10)Why we need to test for regression coefficient? (2 Marks)

Answer 1

1)

CHART TOOLS Sign in Book1 Excel HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Excel QM DESIGN FORMAT FILE Switch Row/ Select Chang Move Column Data Chart Type Chart Typ Location ETTE Add Chart Quick Change Element Layout Colors Chart Stylos Chart Layouts Chart 1 Shelf Length Sales Scatter Diagram 155 173 85 228 186 148 130 156 178 107 120 110 0.8 0.5 1.4 0.9 1.1 1.3 1.6 0.7 0.9 2 1.41.61.8 1.2 08 0.6 0.4 17 18 19 Shelf Length 23 + 100% Sheet1Sheet2

2. The correlation coefficient shows 0.88 and it shows there is a positive relationship between shelf length and sales i.e. as shelf length increases the sales increases

Book1 Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Excel QM Sign in Σ AutoSum . A Cut libri Gerneral Copy- Format Painter в 1 u, 1. 2. Conditional Format as Cell Formatting Table Styles Insert Delete Format Sort & Find & Filter Select 를를娃娃圉Merge & Center, $. % , , Clear- .た >< F4 =CORREL(C4:C15,D4:D15) Shelf Length Sales Correlation Coefficient 0.885407 0.8 1.2 0.5 155 173 85 228 186 148 130 156 178 107 120 110 1.4 0.9 1.1 1.3 1.6 0.7 0.9 10 12 13 15 16 17 18 19 20 21 23 Sheet1Sheet2 + 100%

3. The coefficient of determination is R squared value i.e. 0.78

Book1 Excel FILE From Access From Web From TextConnections HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Excel QM Sign in t ㄧ囹Connections 쇱지 Data Analysis Solver 三囝 Text to Flash Remove Data Consolidate What-If Relationships Group Ungroup Subtotal Columns ll Duplicates Validation From Other Existing Refresh AllEdit Links Analysis Connections All. Edit Links 亂Sort Filter "Reapply Get External Data Sort & Filter Data Tools lysis 011 4 0.8 1.2 0.5 155 173 85 228 186 148 130 156 178 107 120 110 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.885407 0.783945 0.76234 19.54663 12 1.4 1.1 10 1.3 12 13 ANOVA 0.7 0.9 F gnificance F MS Regression Residual Total 1 13863.29 13863.29 36.2846 0.000128 10 3820.709 382.0709 11 17684 15 16 17 18 19 20 21 Coefficientsandard Ern t Stat P value Lower 95%Upper 95% wer 95.07pper 95.0% 44.96203 18.01216 2.496204 0.031652 4.828437 85.09561 4.828437 85.09561 93.67089 15.55047 6.02367 0.000128 59.02229 128.3195 59.02229 128.3195 Intercept Shelf Length 24 25 Sheet1Sheet2 + 100%

It shows that 78% of the variability of sales is explained by the input shelf length

4. Regression line

Sales= 44.93+ 93.67*Shelf length

That means with one unit increase of shelf length the sales increase by 93.67 times and added with 44.93 constant

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