The following table shows the annual sales revenue of 12 firms and their expenditure on the market research.Sales revenue (£ 000) Expenditure on market research (£ 000) 24 1.2 20 0.8 18 1.1 14 0.8 19 0.9 13 0.5 25 1.3 26 1.5 30 1.4 34 1.6 24 1.2 20 0.8Calculate the Pearson correlation coefficient between the two variables, to two decimal places.Comment of the strength of the relationship revenue and expenditure.Find the equation of the the least-squares regression line, assuming sales revenue is the dependent variable (Y) and expenditure is the independent variable (X) to 2 d.p.Use your estimated regression equation in 22 to predict sales revenue if expenditure on market research is: £700. Use your estimated regression equation in 22 to predict sales revenue if expenditure on market research is: £2,000.

Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.1. The data shows annual sales revenue of 12 firms and their expenditure on the market research. Let X be the expenditure , and Y be the sales revenue. The sums are, x y x2 y2 xy 1.2 24 1.44 576 28.8 0.8 20 0.64 400 16 1.1 18 1.21 324 19.8 0.8 14 0.64 196 11.2 0.9 19 0.81 361 17.1 0.5 13 0.25 169 6.5 1.3 25 1.69 625 32.5 1.5 26 2.25 676 39 1.4 30 1.96 900 42 1.6 34 2.56 1156 54.4 1.2 24 1.44 576 28.8 0.8 20 0.64 400 16 ∑x=13.1 ∑y=267 ∑x2=15.53 ∑y2=6359 ∑xy=312.1 The Pearson correlation coefficient between the two variables is, r=n∑xy-∑x∑yn∑x2-∑x2n∑y2-∑y2=12×312.1-13.1×26712×15.53-13.1212×6359-2672=247.5272.0850=0.9096≈0.91 Therefore, the Pearson correlation coefficient between the two variables is 0.91.2. The value of correlation coefficient is 0.91 which is closer to 1 indicating that there is strong positive relationship between the relationship revenue and expenditure. Therefore, there is strong positive relationship between the relationship revenue and expenditure.3. The slope is, b=n∑xy-∑x∑yn∑x2-∑x2=12×312.1-13.1×26712×15.53-13.12=247.514.75=16.77966≈16.78 The intercept is, a=∑y-b∑xn=267-16.77966×13.112=47.18645412=3.93220≈3.93 The equation of the the least-squares regression line, assuming sales revenue is the dependent variable (Y) and expenditure is the independent variable (X) is, Y^=a+bX=3.93+16.78X Therefore, the equation of the the least-squares regression line is Y^=3.93+16.78X.